I called this a brief description because the Torah only lists four of the eleven ingredients, the remainder of which were left to Halacha Le'Moshe MiSinai.
1. Would you say that there is a mitzva to make Ketores? The Smag (167) holds that the mitzva is to fabricate ketores and to use it; as he explains later (last line of Mitzvah 192), he holds they are both equal parts of one mitzvah. On the other hand, the Rambam and the Chinuch hold there is no mitzva to make the ketores. The Mitzva is to burn the ketores at the proper time and place. The Rambam and the Chinuch hold that making the ketores is just a hechsher; you're going to need ketores, so you'd better make it, and the way to make ketores is..... The Smag holds that the fabrication is not merely a hechsher, it is part of the mitzva; it is an equal part of the mitzvah, as you can see in the way he writes the Remez of Mitzva 167. I would say that according to the Rambam and Chinuch, the Avtinases did not make a bracha on their work, while according to the Smag, they did. This is reminiscent of the Machlokes Bavli and Yerushalmi about making the Sukkah.
In any case, we all have the minhag to read the braisa that describes the making of the Ketores. Some read it every day, some only on Shabbos. But everyone agrees it's a good thing to read it; In fact, the Rama in 132 says that the only reason Ashkenazim don't read it every day is because Chazal say that if one skips one ingredient, he violates a very serious issur. During the week, people are rushed and daven too quickly, and if one said the parsha of ketores and skipped one ingredient, it would be a very bad thing. So we limit it to Shabbos, when only tipshim daven quickly, so we can say it calmly and carefully. Indeed, the Magen Avraham says that Talmidei Chachamim should say it every day.
I always wondered, why on earth are we reading the Braisa that describes the preparation of the ketores? If you want the zechus of a korban, you should read the halachos of the sacrificing, the hakrava, not the preparation. You want a korban chatas? You don't have to read about raising sheep. You read about where you shecht it and so forth. So why are we reading about how to make ketores? For the mitzva of limud hatorah, the time would be better spent learning something be'iyun, instead of just reading a Braisa. Learn a Ketzos instead! For the mitzva of haktara, say the parsha that talks about the actual avoda of haktara. (As I discuss below, the Chasam Sofer's teshuva in OC 159 seems to hold like this.)
At least according to the Smag, we have a teretz on this question, because the Smag holds that the making of the Ketores and the burning of the Ketores are two equal halves of one mitzvah. According to the Rambam and Chinuch, the question remains.
2. We are told (Krisus 6b) that a person that makes the Ketores and fails to include any one ingredient is subject to a divine punishment of untimely death. Is this for making it, or for burning it in the Azara? The answer is that 99% of the meforshim hold there are two issurimg: making it and burning it. However, Rashi in Krisus there implies that there is no punishment for burning it except for on Yom Kippur. The Pirush on the Rambam called Orah Ve'Simcha (5 Avodas Yom Hakppurim 25) says that the Rambam holds like that as well, that one is chayav missa for burning incomplete ketores only on Yom Kippur. He says that Rashi holds that there isn't even a punishment of missa for making incomplete Ketores the whole year, only for burning it on Yom Kippur. The Rambam, he admits, holds there is a separate punishment for making it at any time. But all the other meforshim agree that there is a chiyuv all year for making incomplete ketores, and all year for burning it. (see, e.g., Mishna Lemelech 2 Klei Hamikdash 3 who gets very upset about this whole discussion.)
3. The Gemara in Yoma 38 and Shkolim 14 says that the family that made the ketores, Beis Avtinas, was praiseworthy, because their family tradition was that no Avtinas woman left the house wearing perfume, so that nobody should suspect that they had benefited from the Ketores. Any woman marrying into the family was warned about this minhag and had to agree to do so. Lately, some communities of Bnei Torah have begun to discourage women from wearing makeup and perfume outside of the house. They feel it is inappropriate, because it might engender inappropriate thoughts in other men. This extends the Avtinus chumra to all of Klal Yisrael, which I think is sad. There's enough ugly in the world as it is, and we don't have to add to it.
4. The Mishna in Yoma 26a says that while other tasks done in the Beis Hamikdash were allotted by daily lottery, this was not the case with the avoda of burning the Ketores. In this case, the lottery master would announce "Those who have never done the Ketores may come to this lottery." The reason for this restriction is that doing the avoda of the Ketores makes the person wealthy, and everyone deserves a chance. The source for this is the passuk in Devarim 33:10-11,
6. What about those Pittum Haketoreses that are written by a sofer on parchment? Is this completely abnormal? No. It is not. It is a time honored custom among the Sfardim and the Kabala oriented. There are mekoros for this. A man named Moshe ibn Machir, who was the Rosh Yeshiva at a Yeshiva called Ein Zeisim, near Tzfas, in the time of the Arizal, wrote a sefer called Seder Olam. This is a highly respected sefer. In fact, our version of Modeh Ani was introduced by him in this sefer. In the same sefer, he says that one should write the Pittum Haketores on Klaf in Ashuris- and that he takes responsibility for the fulfillment of your wishes:
In fact, the Zohar (Vayakhel) talks about it in the same superlatives. He says that if people realized the supernal benefit of saying Pitum Haketores with deep comprehension, and if they knew how precious it is before Hashem, they would take the words and make them into a golden crown for their heads.
Then there's Reb Chaim Falagi's Kaf Hachaim, in which he tells us to write it on klaf in Ashuris like a sefer Torah and to read it, because it will make you wealthy and immune to parnassa problems.
So, for some, it is a time-honored and worthy minhag. (I saw some available on the web. They start at around 500, but 900 and upwards is more common. That's American dollars.)
For a talmid of the Litvishe mesora, doing this would be as appropriate as eating grasshoppers.