Combine eggs, milk, and water in a large bowl. Whisk to combine. Gradually add flour, salt, and black pepper, if using. Continue whisking until smooth. Let batter rest at room temperature, one hour, before using, or up to 1 day in advance, kept in the refrigerator.
Preheat oven to 475°F. Place a standard 6-cup popover pan on a parchment-lined sheet pan on the middle rack.
When oven is preheated, carefully remove popover pan, brush quickly with butter, and divide batter among all six cups. Top with cheese; batter and cheese will come to the top of each cup.
Return to oven and bake until popovers are puffed and golden and still slightly soft in the centers, about 25 to 28 minutes. Serve immediately.
