Whisk together eggs, salt, and pepper. Melt butter in a non-stick pan over medium heat. Pour in egg mixture. As the eggs set, gently push the cooked portions towards the center, tilting the pan to allow the uncooked egg to flow underneath.
Once the eggs are mostly set but still slightly moist on top, sprinkle the black-eyed peas, white cheddar cheese, peppers, baby spinach, and red pepper flakes over one half of the omelette.
Carefully fold the other half of the omelette over the filling. Cook for another 1-2 minutes, or until the cheese is melted and the omelette is heated through.
Serve immediately.
