Preheat the broiler.
In a large (15-inch) oven-proof skillet, heat 1 tablespoon of the oil. Cook the sausage over high heat, breaking it apart with your spatula into 1-inch pieces (or smaller), until browned, about 5 minutes. Remove to a plate.
Add the remaining oil to the skillet. Saute the onion and peppers over medium heat, scrapping up any brown bits from the bottom of the pan, until very soft and caramelized, about 10 minutes.
Meanwhile, in a large mixing bowl, beat the eggs with the remaining salt until the yolk and whites are very well combined.
Add the sausage back to the pan, season with ½ teaspoon salt, and arrange the in an even layer. Reduce the heat to low and pour the eggs over the sausage and vegetables, making sure the pan is evenly coated with eggs. Cook until the sides are set and there’s just a shallow layer of uncooked eggs on the top, 5 minutes.
Sprinkle the mozzarella and oregano over the top, if using, and transfer the pan to the broiler. Cook for 2 minutes, until the top is cooked and beginning to lightly brown. Remove from the oven and allow the frittata to sit in the pan for 5 minutes before slicing. Cut into wedges and serve alongside a simple salad as breakfast, lunch, or dinner.