Prep: 1. Preheat oven to 425. 2. Remove sausage from casing (if necessary). Grate cheese. Make: 1. Heat 1 teaspoon of oil in a large oven proof skillet over medium-high heat. Cook sausage, breaking up with a spoon, until golden and cooked through. Using a slotted spoon, transfer to a plate. Wipe out skillet. 2. Return cleaned skillet to the stove and heat remaining tablespoon oil over medium heat. Add beaten eggs and stir for one minute. Let cook undisturbed so that eggs set on the bottom of the pan. 3. Sprinkle sausage, parmesan and arugula on top. 4. When the edges are set, transfer to the oven and cook until set throughout, about 6 minutes.
If you don't have an oven proof skillet you can do this only on the stove top by covering the eggs while they cook. Depending on the size of your skillet it will take about 10-12 minutes to cook through.