Heat 1 teaspoon olive oil in a 10-inch oven-proof skillet over medium heat. Add the bacon and cook for 2 minutes. Add the mushrooms, 1 teaspoon salt, and ½ teaspoon pepper. Cook, stirring occasionally, until the mushrooms have released their liquid and the liquid has evaporated, 12-14 minutes. Remove pan from the heat.

Preheat the oven to 400 degrees.

Lightly beat the eggs and pour over the mushrooms and bacon. Sprinkle 1 cup Parmesan cheese over the top of the eggs and bake for 10 minutes or until the eggs are set.

Toss the arugula with 2 tablespoons olive oil, the balsamic vinegar, remaining ½ cup Parmesan cheese, and a large pinch of salt and pepper. Put on top of the frittata and serve.