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. Sprinkle half of the cheddar cheese evenly over the tortilla.
Spoon the scrambled eggs over the cheese, then top with the remaining cheese. Place the second tortilla on top.
Cook for about 2-3 minutes until the bottom tortilla is golden brown and the cheese begins to melt. Carefully flip the quesadilla using a large spatula and cook for another 2-3 minutes on the other side until golden brown and crispy.
Remove from the skillet and let it cool for a minute before cutting into wedges. Serve with sour cream and salsa if desired.