Preheat oven to 350 degrees Fahrenheit. Prepare artichokes according to package directions. Set aside.
In a cast iron skillet, heat olive oil over medium-high heat. Add onions, garlic, oregano and artichokes. Sauté 3-5 minutes or until vegetables are wilted. Remove skillet from heat and set aside. Generously grease a 9” x 13” baking dish and coat the bottom with ¼ cup Parmesan cheese. Spoon the artichoke mixture evenly over the bottom of the dish. In a mixing bowl, combine beaten eggs, milk, salt, pepper and nutmeg.
NOTE: Be careful when adding salt to this recipe since Parmesan cheese normally has high sodium content. Blend well, then add Monterey Jack cheese and ¼ cup Parmesan cheese. Distribute egg mixture over the artichokes and spread evenly. Bake, uncovered, for 25 minutes.
Remove dish from oven, sprinkle evenly with remaining Parmesan cheese and continue baking until Frittata is puffed and golden brown, approximately 5 minutes.