Melt the butter in a medium nonstick skillet over medium heat.
In a small bowl, whisk together the eggs, salt and pepper.
Pour the egg mixture into the skillet to coat the bottom.
Place the tortilla on top of the egg, then flip the tortilla over so that both sides of the tortilla are covered in the egg mixture.
Continue to cook the eggs and tortilla for 1-2 minutes, or until the eggs are completely set.
Slide a spatula under the egg, then flip the whole tortilla and egg over to cook the other side.
While cooking, place the sliced cheese along the edge of the tortilla closest to you, then layer the ham on top of the cheese.
Continue cooking until the bottom is golden, about 1 more minute, then place the tortilla on a plate.
Roll the tortilla into a tight wrap, starting with the side that has all the filling. Cut in half crosswise and serve warm.