Heat a non-stick skillet over medium heat and add a small amount of butter.
Crack one egg into the skillet, season with salt and pepper, and cook until the white is set but the yolk is still runny. Remove and set aside. Repeat with the second egg.
In the same skillet, place one tortilla and sprinkle half of the shredded cheese over it.
Place the fried eggs on top of the cheese and then add the avocado slices.
Sprinkle the remaining cheese over the avocado and top with the second tortilla.
Cook for 2-3 minutes on each side until the tortilla is golden brown and the cheese is melted.
Remove from skillet, cut into wedges, and serve hot.