Why do we split up the Hallel in the Haggadah and say two paragraphs of Hallel by Magid and the rest of Hallel after the Birchat Hamzon? Why not complete all of Hallel initially?
Chabad.org - Rabbi Baruch S. Davidson - quoting the Abarbanel in his Sefer Zevach Pesach says that the first part of Hallel talks about miracles that already occured. The Second part talks about miracles that will occur when Mashiach comes.
In his commentary Zevach Pesach on the haggadah, the great Spanish scholar Don Isaac Abarbanel (1437–1508) answers this question.
The exodus from Egypt, the crossing of the sea, and the giving of the Torah are all mentioned in the first two chapters of the Hallel. At the Seder, after reciting these two chapters, we say the Asher Ge’alanu (“who has redeemed us”) blessing, and we eat the matzah—both of which commemorate the miracles and redemptions of the past.
The following chapters of the Hallel mention the miracles which will happen in the future, with the coming of Moshiach—a topic of their own, worthy of being discussed separately. They are appropriately recited towards the end of the Seder, when we have just greeted Elijah the prophet, who will herald the coming of Moshiach, and when we focus on our anticipation of, yearning for and belief in the messianic redemption.
Sefer Abudirham in its comments on the Haggada, explains that:
כדי להדר בו את כוס שני שכוס ראשון מהדרי בקידוש וכוס שני מהדרי במקצת ההלל שההגדה אינה אלא ספור דברים בעלמא וכוס שלישי מהדרו בברכת המזון וכוס רביעי מהדרו בהשלמת הלל
[Hallel is split] in order to glorify the second cup, for the first cup is glorified with Kiddush, the second cup is glorified with part of Hallel for [the story part of Maggid] is just telling over a story, and the third cup is glorified with the Grace After Meals, and the fourth cup is glorified with the rest of Hallel.