Answer: This question has already been discussed by the Maharshal (Rabbeinu Shlomo Luria, one of the foremost Acharonim who lived approximately five-hundred years ago in Eastern Poland and authored the Sefer Yam Shel Shlomo and others) in his responsa (Chapter 97) and writes that if one becomes obligated to recite an after-blessing on any given food one eats and then becomes obligated to recite the “Asher Yatzar” blessing, one should recite the “Asher Yatzar” blessing first and only then recite the after-blessing on the food based on the rule, “The more frequent of two Mitzvot is performed first.” Thus, the “Asher Yatzar” blessing is recited consistently several times every day while regarding an after-blessing on food, there is a possibility that one will not become obligated to recite it for several days.
Hagaon Ya’abetz (Rabbeinu Yaakov Emdin ben Tzvi, son of the Chacham Tzvi, who lived approximately three-hundred years ago in Germany) writes regarding this ruling: “In my humble opinion, who says that this blessing (an after-blessing on food) is any less frequent that the other (the “Asher Yatzar” blessing)? On the contrary, for most people, eating and drinking is more common than using the facilities. Thus, if we are ruling based on the frequency of the blessings, indeed, the after-blessing on food should be recited before the “Asher Yatzar” blessing.” He nevertheless concludes that he agrees with the Maharshal’s ruling but not because of his reasoning that the “Asher Yatzar” blessing is more common; rather, it is for a different reason which is that since this individual has now become obligated to praise and thank Hashem for the perfection of one’s body through the “Asher Yatzar” blessing, one must therefore surely recite the blessing which one has become obligated to recite now since one will not be able to recite the after-blessing immediately upon finishing to eat in any case, for that time has already elapsed. Thus, one should recite the “Asher Yatzar” blessing and only then recite the after-blessing on food. Many other great Poskim discuss this issue and provide sources for either option.
Halachically speaking, Maran Rabbeinu Ovadia Yosef zt”l writes (in his Yabia Omer, Volume 9, page 183) that one should indeed recite the “Asher Yatzar” blessing first and only then recite the after-blessing on the food, either because of the Maharshal’s reason or because of the reason quoted by Hagaon Ya’abetz.