In Limud Torah on Milah
( limudtorah.jewishweb.org )we brought that the Minchas Chinuch asks: How can the Rosh say that you make L'Hachniso LBriso Shel Avraham Avinu before the Pria, so that it should be said before the end of the Mitzva? Since Avrahom Avinu did not receive the Mitzva of Pria, only of Mila, so the part that's referring to in the Bracha was already done, so why is it's considered being done before the Mitzva.

IMHO we can answer: What is the nature of the addition of Priah? Is it an added Mitzva or an extension of the original Mitzvah? the Mishna says that on that does Mila without Priah, it's like he doesn't have a Milah. From here it would seem that it's the extension of the original Mitzva and there is no Mila done without Priah. Not that you did one Mitzva but didn't fulfill the second Mitzva.

Therefore, before you did the Priah, you hadn't done the Mila part either. By doing the Priah, you are from this point making the Mila into a Mila. Therefore, saying the Bracha before the Priah is like your making the Bracha before the Mila.