In a large skillet, heat butter and oil over low heat. Slowly cook the onions, stirring occasionally until the onions become translucent, about 8-10 minutes. Stir in garlic powder, oregano and artichokes.
Whisk the eggs in a bowl with heavy cream, Parmesan cheese, salt and pepper. Then pour into the skillet with the onion artichoke mixture. Sprinkle with Mozzarella cheese.
Cook the eggs undisturbed until the edges begin to pull away from the edge of the pan and begin to set. Gently lift the edges of the egg and tilt the pan so the uncooked egg runs under the cooked part and cook for another minute or so.
Transfer to the oven and bake until completely set through, about 4-5 minutes. Garnish with chives or green onion and enjoy.