Preheat oven to 425 degrees F. Line two baking sheets with silicone baking mats or parchment paper.
Place the butter, milk, water, salt, and pepper in a medium saucepan and bring to a boil over medium-high heat. Add all of the flour at once, reduce heat to medium-low and stir with a wooden spoon until the mixture forms a ball and appears to dry out (a film or “crust” will develop on the sides and bottom of the pan), another 2 to 3 minutes.
Immediately place the dough into a mixing bowl and beat on low until it stops steaming and is just warm to the touch, approximately 1 minute.
Increase mixer speed to medium and add the eggs, one at a time, beating well after each until fully incorporated and scraping the sides and bottom of the bowl as needed. Add the cheese and mix until thoroughly combined, about 1 minute. The final dough will appear smooth, creamy, and shiny.
Transfer the dough to a pastry bag fitted with a large round piping tip (I recommend Ateco #809), and pipe 1-2 tablespoons of dough onto the prepared sheets. Alternately, use a medium cookie scoop, drop the dough onto the prepared baking sheets, leaving 2 inches between them. You can wet your hands and gently smooth out the scoops, if you’d like.
Bake for 10 minutes, reduce oven temperature to 350 degrees F, and continue to bake until puffed and golden brown, an additional 5 to 10 minutes. Allow to cool for at least 5 minutes, then serve warm or at room temperature.
Notes
You can substitute grated Swiss or Parmesan cheese for the Gruyere.
You can substitute ⅛ to ¼ teaspoon cayenne pepper for the black pepper if you prefer an all-over spicier flavor.
You can use all water instead of half water, half milk.
You can mix the eggs into the dough using a simple wooden spoon, a hand mixer, or a stand mixer.
The dough can be portioned onto the baking sheet using a pastry bag with piping tip, a cookie scoop, or two spoons.
The baking time listed is for 1 to 2-inch gougères; if you choose to make them larger, I would reduce the initial bake time at 425 degrees to 5 minutes, then bake at 350 degrees until finished.
Freshly-baked gougères are best eaten the same day that they are made, though you can store in an airtight container at room temperature for up to 2 days and eat at room temperature, or re-heat in a 325-degree oven.
To Freeze Gougères: Prepare the dough and pipe onto a baking sheet. Place the baking sheet in the freezer until the gougères are completely frozen, 1 to 2 hours. Once frozen, transfer to a ziploc freezer bag and store in the freezer for up to 2 months. To bake from frozen, bake at 425 degrees for 5 minutes, then at 350 degrees for 15 to 20 minutes.
To Freeze Baked Gougères: Cool completely after baking, then place in a ziploc freezer bag and freeze for up to 2 months. To reheat, place in a 350-degree oven for 6 to 8 minutes, or until warmed through.