Whisk 2 tablespoons olive oil, the vinegar, 1/4 teaspoon salt, and pepper to taste in a medium bowl. Add the arugula, olives and roasted red peppers but don't toss yet (you don't want the arugula to wilt). Set aside while you prepare the omelets.
Whisk the eggs, milk and a pinch of salt in a bowl. Heat a medium nonstick skillet over medium heat. Add about 1 teaspoon olive oil, then pour in 1/2 cup of the egg mixture and stir gently with a rubber spatula to distribute the egg in the bottom of the pan. Cook until the eggs are just set but the underside is not brown, about 4 minutes, then slide the omelet onto a plate. Repeat to make 3 more omelets, adding about 1 more teaspoon oil to the skillet between each.
Toss the arugula salad, then pile on top of the omelets. Scatter the feta and prosciutto on top.