Heat oven to 350° F.
Heat 1 tablespoon of the oil in a large, ovenproof nonstick skillet over medium heat. Add the scallions and cook, stirring, for 1 1/2 minutes. Add the prosciutto and cook, stirring occasionally, until slightly crisp, 3 to 4 minutes.
Meanwhile, in a medium bowl, whisk together the eggs, milk, Parmesan, and pepper. Add the cooked scallions and prosciutto. Pour the egg mixture into the skillet and stir to distribute the ingredients. Bake until browned around the edges and puffed (a knife should come out clean), 15 to 20 minutes.
Meanwhile, divide the arugula among individual plates. Drizzle with the remaining olive oil, sprinkle with the salt, and top with the goat cheese. Cut the frittata into triangles and serve with the salad.
Tip: If you don’t own an ovenproof nonstick skillet, use a seasoned cast-iron pan instead.