Preheat oven to 400 degrees F. In a large bowl whisk together the eggs, basil, salt, and pepper. Heat oil in an oven-safe 10-inch skillet over medium heat. Add sweet pepper and meatballs; cook and stir for 4 minutes. Add egg mixture. Cook over medium heat. As mixture sets, run a spatula around the edge of the skillet, lifting the egg mixture so uncooked portion flows underneath. Continue cooking and lifting edges until egg mixture is almost set (surface will be moist). Sprinkle with cheese. Bake for 5 minutes or until top is set.