Grease a 6-tin muffin pan with butter and cooking spray.
Whisk eggs, milk, flour, salt, and cayenne pepper together in a small bowl until smooth. Pour batter into each muffin tin, filling to about 3/4 of the way up the sides. Sprinkle about 1 teaspoon of grated Cheddar cheese atop each popover.
Place pan in a cold oven. Heat to 450 degrees F (230 degrees C) and bake until puffed and well-browned, about 30 minutes.