Melt butter in a heavy bottomed skillet over medium low heat.
When butter is melted pour beaten eggs into the skillet, season with salt and pepper.
Cook over low heat until eggs are set and no longer runny when you tilt the pan.
Top eggs with about a tablespoon of cheese and then the flour tortilla. Gently press tortilla down onto the surface of the eggs.
Using a spatula, carefully flip the egg/tortilla so that the tortilla is on the bottom, and the egg is now on top.
Top the egg with the remaining shredded cheese, the sliced ham and some green onion or chives.
Use spatula to carefully fold the tortilla in half.
Continue to cook until tortilla is golden brown.
Flip tortilla over and continue to cook until the second side is a crispy golden brown, and the cheese is completely melted, hot and gooey.
To serve, cut quesadilla into three wedges and top with a dollop of sour cream, a sprinkle of chives or green onion and a side of your favorite salsa.