Preparation: Put red pepper under the broiler or directly on a gas flame until charred and blackened all over, about 10 minutes altogether. Peel, cut the pepper in half, seed, and cut lengthwise into 1-inch-wide strips.
Wash and trim the beans. Cut the onion into thin slices. Grate the cheese.
In a large pot of boiling water, cook the beans until tender, 5 to 10 minutes. Drain and refresh under cold, running water; then drain again.
Heat the oil in a 12-inch round baking pan or ovenproof frying pan over medium heat. Add the onion and saute until softened, about 4 minutes. Remove from the heat. Arrange the beans over the onion slices. Put the red pepper strips on top of the beans, arranging them in a star design.
Cooking: Heat the oven to 425 deg F. Lightly whisk the eggs with salt and pepper to taste. Pour the eggs over the vegetables and sprinkle with the cheese.
Bake in the preheated oven until the sides puff up, the eggs are a light golden color, and a knife inserted into the center comes out clean, about 20 minutes.
SERVING: Serve hot, warm, or at room temperature, cut into wedges.