Pesachim 121B

רבי שמלאי איקלע לפדיון הבן, בעו מיניה: פשיטא על פדיון הבן ״אשר קדשנו במצותיו וצונו על פדיון הבן״⁠ — אבי הבן מברך. ״ברוך ... שהחיינו וקיימנו והגיענו לזמן הזה״, כהן מברך, או אבי הבן מברך?

The Talmud discusses another case concerning the order of the blessings: R' Simlai attended a redemption of the firstborn son. The celebrants raised a dilemma before him with regard to the blessings. First they noted that it is obvious that the blessing over the redemption of a firstborn son, which is: Who sanctified us with His mitzvot and commanded us over the redemption of the firstborn son, is certainly recited by the father of the son, as he is the one obligated to redeem his son. However, with regard to the second blessing: Blessed are You, Lord our God, King of the universe, Who has given us life [sheheḥeyanu], sustained us, and brought us to this time, does the priest recite this blessing, or does the father of the son recite it?

כהן מברך ⁠— דקמטי הנאה לידיה, או אבי הבן מברך ⁠— דקא עביד מצוה? לא הוה בידיה, אתא שאיל ביה מדרשא. אמרו ליה: אבי הבן מברך שתים. והלכתא: אבי הבן מברך שתים.

The Talmud explains the two sides of the dilemma. It can be suggested that the priest recites the blessing, as he benefits from the 5 sela he receives when the boy is redeemed. The blessing of sheheḥiyanu is generally recited by the one who receives the benefit. Or, perhaps the father of the son recites sheheḥeyanu, as he is the one who performs the mitzva. R' Simlai did not have an answer readily available, and he went to ask this question in the study hall. The scholars said to him that the father of the son recites the two blessings: Over the redemption of the son and sheheḥeyanu. The Talmud concludes: And the halakha is that the father of the son recites two blessings.