Heat a 9 to 11" -inch crepe pan over medium heat. Lightly grease with the butter.
Pour enough batter into the pan and swirl to evenly coat the surface. Cook the crêpe until it begins to bubble and the edges begin to brown, about 1 to 2 minutes. Flip.
Crack an egg onto the surface of the crêpe and break up with a spatula (you can pre-beat the egg, if desired). Spread the egg out evenly and season with salt and pepper to taste. Let the egg cook just until it starts to set before sprinkling the surface with a bit of cheese. Place a piece of ham on one half of the crêpe. Monitor the heat (you may need to turn it down slightly).
Once the cheese begins to melt and the egg has almost fully set, fold the crêpe in half. Sprinkle with a bit more cheese. Fold the crêpe again in half to form a triangle. Use a spatula to make a crease in the middle of the crêpe to help you fold it over.
Flip the crêpe over to warm through. Once the cheese has completely melted and the egg is just cooked, serve immediately.
Continue making and filling each crêpe. These crêpes are best served when they come out of the pan; however, you can place them onto a tray and hold them in a warm oven until you are finished making all four.
Serve the crêpe by itself or with a nice salad, such as this Carrot Salad.