Preheat oven to 425°F. Line baking sheets with baking parchment or silicone mats.
In a large heavy-bottomed saucepan over high heat, bring water, milk, salt, and butter to a rolling boil.
Immediately add the flour, reduce heat to medium-low, and stir vigorously until a dough forms and dries out a bit, about 2 minutes.
Transfer dough to stand mixer, fitted with the paddle attachment. Let dough cool for one minute.
Add eggs, one at a time, and beat on medium speed until dough is thick and shiny. Wait until one egg is fully incorporated before adding the next.
With the mixer still on medium speed, mix in cheese.
Spoon out dough by the heaping teaspoonful, placing about 2 inches apart on the prepared baking sheets.
Place in oven. Immediately reduce heat to 375°F and bake 25 to 30 minutes, rotating the sheets from top to bottom and front to back halfway through, or until puffed with a crisp golden brown shell.
Serve immediately.