Why ashkenazim don’t say the first berachah before Hallel on Passover seder night whereas they do say the berachah after the Hallel?
This question is asked by the Ramban (Pesachim 117b), who proves from the fact that the last berachah is recited that the first one should also be recited.
However, our custom follows the ruling of the Geonim, whereby only the last berachah is recited, and not the first.
The reason for this is the hefsek (interruption) of the meal (Machzor Vitri), or according to many Rishonim because this Hallel is different in nature to others (see Ran and other Rishonim), and it is considered reading from the Torah and Shira (song) rather than the standard obligatory Hallel (see also the famous passage of the Brisk Rav about this topic).
For this reason, only the last berachah, which is part of the praise of Hallel, is recited, and not the first which is a berachah over the mitzvah of reciting Hallel.