Preheat the oven to 350°. Heat the olive oil in a medium oven-safe skillet over medium heat. Add the onions, reduce the heat to low and cook the onions until they’re golden brown and caramelized, 20 to 25 minutes.
Season the onions to taste with salt and red pepper flakes. Add the arugula and cook until wilted, 1 to 2 minutes. Raise the heat to medium high.
In a medium bowl, whisk the eggs, egg whites and milk to combine. Pour the mixture into the pan and let it cook for 2 to 3 minutes to set the base. Sprinkle the crumbled goat cheese on top of the egg mixture.
Transfer the pan to the oven and bake until the frittata is set, 15 to 20 minutes. Let cool for 5 minutes before serving. The frittata can be served warm, at room temperature or chilled.