Preheat an oven to 400 degrees F (200 degrees C). Grease a 9x13 inch baking pan.
In a large skillet over medium heat, cook and stir the sausage and onion until the sausage is well browned, about 10 minutes. Drain; set aside to cool slightly.
Stir together the Swiss cheese, Parmesan cheese, egg, and milk in a large bowl. Stir in the biscuit mix, margarine, and parsley. Add the sausage mixture; stir until well combined. Pour the mixture into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 35 minutes. Serve warm or cold.