Cut the peppers in half and remove and discard the ribs, seeds, and stems. Cut them into strips about 2 inches long and ½ inch wide. Set aside.
In a flameproof, nonstick 12-inch omelet pan or skillet over medium-low heat, warm the ¼ cup olive oil. Add the onion and sauté until wilted, about 8 minutes. Using a slotted spoon, transfer the onion to a dish and set aside. Be sure to drain any oil in the dish back into the pan.
Warm the oil again over medium-low heat. Add the bell peppers and sauté gently until soft, 15 to 20 minutes, tossing occasionally to cook them evenly.
Meanwhile, in a bowl, beat the eggs lightly with a fork. Stir in the parsley, cheese, salt, and pepper.
When the peppers are cooked, combine them with the onion. When it has cooled enough not to cook the eggs, stir the pepper and onion mixture into the egg mixture.
Preheat a broiler. Wipe the pan clean and pour the 1-½ tablespoons oil into it. Use a pastry brush to oil the sides of the pan as well as the bottom to insure that the frittata will not stick to the pan when you unmold it. Place the pan over medium heat. When it is hot enough to make the eggs sizzle, add the egg mixture, using a fork or spoon to distribute the vegetables evenly. Immediately reduce the heat to low and cook until the frittata is set but not browned, 12 to 15 minutes. Take care not to overcook the eggs or they will lose their delicacy.
To finish cooking, slide the pan under the preheated broiler 6 inches from the heat. Broil until the top is golden, 1 to 2 minutes. Using a spatula, loosen the edges from the pan and slide the frittata out onto a serving plate. Serve warm or at room temperature, cut into wedges.