Heat a non-stick skillet over medium heat. Add 1 tablespoon of butter and let it melt completely.

Crack the first egg into the skillet and season with salt and pepper. Cook for 2-3 minutes until the whites are set but the yolk remains runny. Transfer to a plate and repeat with the second egg.

Place one flour tortilla in the skillet, sprinkle half of the cheese, layer both fried eggs on top, add avocado slices if using, and finish with the remaining cheese.

Cover with the second tortilla and cook for 2-3 minutes until golden brown. Flip carefully and cook the other side for another 2-3 minutes.

Remove from skillet, let cool for a minute, and slice into wedges. Serve hot with optional toppings.