Heat a non-stick skillet over medium heat and add a pat of butter. Allow it to melt completely.

Crack the first large egg into the skillet, seasoning it lightly with salt and pepper. Cook until the whites are set but the yolk remains runny, about 2-3 minutes. Remove the egg and set aside, repeating with the second egg.

Place one flour tortilla in the now warmed skillet and sprinkle half of the shredded cheese evenly across the top.

Layer the perfectly fried eggs on top of the cheese, followed by slices of creamy avocado. Finish by sprinkling the remaining cheese on top and placing the second tortilla over everything.

Cook for 2-3 minutes on each side, flipping gently until the tortilla is golden brown and crispy, and the cheese has melted.

Cut the quesadilla into wedges and serve immediately.