Preheat the oven to 350 degrees F (175 degrees C). Split English muffins and lay on a sheet pan.

Rub butter into each cavity of a 12-cup muffin tin, then crack an egg into each cavity. Break the yolks unless you want them runny.

Place the English muffins and eggs in the preheated oven on separate racks. Toast the muffins until golden brown, about 3 minutes, then remove. Bake the eggs until set, 10 to 15 minutes.

Lift eggs out of the pan with a spatula and place on English muffins. Top with ham and Cheddar cheese. Serve hot.