Preheat oven to 425°F and line a half sheet pan with parchment.
In a medium pot (use stainless steel and avoid nonstick pans), bring water, unsalted butter, and salt to a boil over high heat. Remove from heat and stir in flour with a wooden spoon, and then return to heat and cook while mixing until a skin forms on the bottom of the pot.
Remove from heat and transfer dough to a stand mixer fitted with a paddle attachment. Mix on medium speed until dough stops steaming and bowl is no longer hot to touch.
Add eggs one at a time, fully incorporating after each. The exact amount of egg you need will vary based on how much moisture was evaporated. Continue until dough falls off the paddle and leaves a "v" shape hanging from the paddle. Add the gruyère and parmesan and mix to incorporate.
Transfer dough to a piping bag fitted with a large round tip. On the lined sheet pan, pipe dough into large rounds (approx. 1 1/2in-2in across). Use a wet finger to smooth out and rough tops.
Bake at 425°F for 15 minutes, then drop the temperature to 375°F and continue for another 20 minutes, until deeply golden brown. Remove and set aside to cool.