Reduce the heat to medium-low and pour in the egg mixture. Let the eggs lightly set before gently moving around the outside edge with a rubber spatula. Tilt the pan to allow the uncooked eggs to fill in at the edge. Continue the process until the eggs are fluffy and only the center is slightly runny.
Remove the pan from the heat and top with asparagus, cheese slices, and parsley. Place in the oven and cook until the eggs are just cooked and the cheese is melted about 2 minutes. Sprinkle with the Piment d'Epelette chilli pepper and serve.