Heat 1 teaspoon oil in a 10-inch nonstick skillet over medium heat. Add bell pepper and cook until tender, about 2 minutes. Add garlic and crushed red pepper; cook, stirring, for 30 seconds. Transfer to a plate. Wipe out the pan.
Whisk eggs in a medium bowl. Stir in artichoke hearts, Parmesan, oregano, salt, pepper and the bell pepper mixture.
Set a rack about 4 inches from the heat source; preheat the broiler. rush the pan with the remaining 1 teaspoon oil; heat over medium heat. Pour in the egg mixture and tilt to distribute evenly. Reduce the heat to medium-low and cook until the bottom is light golden, lifting the edges to allow uncooked egg to flow underneath, 3 to 4 minutes. Place the pan under the broiler and cook until the top is set, 1 1/2 to 2 1/2 minutes. Slide the frittata onto a platter and cut into wedges.