Begin by heating a non-stick skillet over medium heat. Add a small amount of butter and let it melt, gently swirling the pan to coat the bottom evenly.

Crack each egg carefully into the skillet. Season with salt and pepper. Fry for about 3-4 minutes until the whites are set but yolks are runny. Set aside.

Place one flour tortilla in the skillet. Sprinkle half of the shredded cheese, add the fried eggs, and top with avocado and remaining cheese before covering with a second tortilla.

Reduce heat slightly to medium-low. Cook the quesadilla for 2-3 minutes until golden brown, then flip and cook the other side for another 2-3 minutes.

Remove the quesadilla, let it cool for a minute, then cut into wedges. Serve hot with salsa or sour cream.