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.
Lay one tortilla flat in the skillet. Sprinkle half of the shredded 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 the quesadilla for about 3-4 minutes, or until the bottom tortilla is golden brown and the cheese starts to melt. Carefully flip the quesadilla using a spatula and cook for another 3-4 minutes on the other side.
Once both sides are golden and the cheese is melted, remove the quesadilla from the skillet and let it cool for a minute. Cut into wedges and serve with optional toppings.