Begin by heating a non-stick skillet over medium heat. Add a small pat of butter and allow it to melt, swirling it around to coat the surface evenly.

Crack one large egg gently into the skillet and season it with salt and pepper. Cook for about 2-3 minutes, then transfer to a plate.

In the same skillet, lay down one flour tortilla and sprinkle half of the shredded cheese across it. Let the cheese melt for about 1-2 minutes.

Layer the fried eggs over the melted cheese, add slices of avocado, then sprinkle the remaining cheese over the eggs, and cover with another tortilla.

Return the quesadilla to the skillet and cook for 2-3 minutes, checking for a golden brown bottom and melted cheese.

After both sides are golden brown, remove from the skillet, cool slightly, and cut into wedges. Serve immediately.