Bring a small pan of water to a boil; add artichoke hearts. Lower the heat; simmer 3 minutes, then rinse, drain, and pat dry. Set aside. Heat 1 tablespoon olive oil in a 10-inch oven-proof skillet. Add potato and rosemary, and saute until golden and crisp, about 3 minutes. Add artichoke hearts and saute until golden, about 2 minutes. Sprinkle with salt and pepper; set aside. Preheat the broiler.
Lightly beat eggs with salt and pepper. Heat remaining olive oil in the same skillet. Pour in eggs and cook over medium low heat, stirring lightly, just until the bottom is set, about 2 minutes. Arrange artichoke hearts, potato slices, and tomatoes on top; sprinkle with cheeses. Place the skillet under the broiler and cook until golden brown and sizzling, about 2 minutes. Serve garnished with parsley and/or herbs sprinkled on top.