The passuk says הַמּוֹצִיא אֶתְכֶם מִתַּחַת סִבְלוֹת מִצְרָיִם, who will take you from the burdens of Mitzrayim. Since Hashem is talking to Moshe long before they left, the simple meaning of the passuk is that hamotzi is "who is going to take you out." If so, then, הַמּוֹצִיא would be the wrong word to use in the bracha of Hamotzi, which thanks Hashem for the bread we are eating which He brought forth from the ground, not what He will do in the future. Nonetheless, the Gemara in Brachos 38a/b says that lehalacha we do say Hamotzi and not Motzi, and we interpret our verse to mean "I will do something that will inspire future generations to remember that I took them out of Mitzrayim."
The gemara there says that someone told Reb Zeira that Reb Zevid's son was a talmid chacham and an expert in brachos. Reb Zeira said "send him to me, and I'll decide if he's a talmid chacham." When the young man came, Reb Zeira gave him bread and told to to eat it. He said Motzi, not Hamotzi. Reb Zeira said, "this person you call a baki in brachos? Everyone knows that Motzi is a good nusach. If he were a talmid chacham, he should have said Hamotzi, which would be a chiddush in halacha and an interesting pshat in the passuk in Va'eira." Reb Moshe points out, (and I'm pretty sure he was quoting a Rosh which I can't remember at the moment,) that evidently it was expected that a talmid chacham, in a new place, would choose a non-standard novel nusach of Hamotzi just so that he would have the opportunity to say a shiur and show that he knew how to learn.
It is assur to talk or delay unnecessarily between netilas yadayim and hamotzi. But the first Magen Avraham in OC 166 brings an opinion (Rabbeinu Tam) that on Shabbos, this problem is not as serious. The issur hefsek before hamotzi is not like hefsek in davening, where the problem is zilzul, disrespect of the tefilla. Here, the problem is that you might get involved in something else and distracted, and end up not eating at all. On Shabbos, when you have a mitzva to eat, and there's a festive table set, there is no such concern, so go ahead and talk. Actually, he's talking about making kiddush or havdalah before hamotzi, but (as is clear in the Aruch Hashulchan there) the logic pertains just as well to any talking. We don't hold like that, though, le'halacha.
But what about combining the two heteirim? If someone wants to talk in learning before hamotzi on Shabbos, he has two svaros to be meikil- the Rabbeinu Tam/Magen Avraham and the Tshuvos Maharshal/Shlah. Would such a thing be a lechatchila le'halacha? No. Is it worth doing it just to shock and awe people, and then tell them why you did it, just as Rav Zeira expected Reb Zevid's son to do? Yes.
And it would be perfect for this week's parsha. Wash, say ahl netilas yadayim, and say a dvar torah before hamotzi. The Dvar Torah would be to explain that the nusach of Hamotzi is connected to this week's parsha, but at one time, most people said Motzi, not Hamotzi; but Reb Zeira held that a talmid chacham should use the non-standard so he could say a shiur about why he did so and the pshat in the passuk in Va'eira. So you see that it's good to be somech on daas yachid in the bracha of Hamotzi in order to show a chiddush in Torah. Normally, we're not allowed to talk before hamotzi, but we are going to follow Reb Zeira's advice and do so because here, there are two reasons why we can be meikil: Shabbos, according to the Magen Avraham/Rabbeinu Tam, and for divrei torah, according to the Shlah/Mahrshal. Presto! (For those that feel that I am playing fast and loose with the halacha, please do two things: first, please realize that we're not talking about hilchos mikvaos here; and second, see the second picture in the column on the right.)
Speaking of the dinim of hefsek and this week's parsha: There's a sefer from the Dubner Maggid on the parshios. In this week's parsha, he connects Yetzias Mitzrayim to the Rama's din in 119. The Rama in 119 says that there's less of a problem of smichas geula l'tfila on Shabbos. Normally, the requirement that we not interrupt is based on the psukim of ya'ancha next to Hashem sfasai tiftach, and since on Shabbos it's not a time of "tefilla to be saved from yom tzara", the psukim don't apply. The Magid says that on Shabbos we daven for simcha, not to be saved from suffering, and that's pshat in not having a din of tefilla of yom tzara.
So while I wouldn't recommend relying on the Rama regarding geula/tefilla, I think there's a special mitzva to say a dvar Torah between Netilas Yadayim and Hamotzi on Friday night of Parshas Va'eira.