In a small bowl, crack the eggs and whisk them together with a pinch of salt and pepper until well combined.
Heat a non-stick skillet over medium heat and add the butter. Once melted, pour in the whisked eggs. Cook, stirring gently, until the eggs are scrambled and just set, about 2-3 minutes. Remove from heat.
Place one tortilla in the skillet over low heat. Evenly spread half of the scrambled eggs on one half of the tortilla, then sprinkle half of the cheese on top. Fold the tortilla over to cover the filling.
Cook for about 2-3 minutes on each side, or until the tortilla is golden brown and the cheese is melted. Repeat with the second tortilla and remaining ingredients.
Slice each quesadilla into wedges and serve warm with salsa or hot sauce if desired.