Heat the oil in a medium skillet over medium-high heat. Add the onion and cook until translucent, about 3 minutes. Add the sausage and cook until brown, about 5 minutes. Set the pan aside to cool.
In a large bowl, whisk together the eggs, milk, salt and pepper, to taste, until smooth, about 20 seconds. Add the red pepper, 1 cup of Gruyere cheese and 1/4 cup of parsley. Stir in the onion mixture. Pour the batter into the prepared pan. Sprinkle with the remaining cheese. Bake for 20 to 25 minutes or until golden brown.
Cut the baked omelet into wedges and sprinkle with remaining parsley before serving.
Cook's Note: To make individual servings, divide the batter between 4 buttered 8-ounce ramekins. Bake for 15 to 18 minutes.