Step 1Heat the broiler. Melt the butter in a 10-inch nonstick skillet over medium-low heat. Add the onion and salt, then cover the pan and cook until the onions have softened, about 5 minutes. Remove the lid and continue to cook, stirring occasionally, until the onions have lightly browned, about 10 minutes. Stir in the prosciutto and cook until softened, 2 to 3 minutes.
Step 2While the onions are cooking, beat the eggs with a fork in a mixing bowl just until the yolks and the white are thoroughly mixed, but don't overbeat, which can make the frittata dry. Beat in the parsley and one-fourth cup Parmigiano-Reggiano.
Step 3Add the egg mixture to the pan with the onions and prosciutto and stir well to combine. Reduce the heat to low and cover the pan. Cook, without stirring, until the eggs have set, leaving only a top layer uncooked, about 10 minutes. Place under the broiler until the top is browned and puffy, 1 to 2 minutes.
Step 4To unmold the frittata, let it cool slightly in the pan. Use a spatula to loosen it along the sides, and then bang it firmly on a cutting board to release the underside. Slide it out onto a serving plate. Serve either hot or at room temperature. If you're going to refrigerate the frittata, let it warm to room temperature before serving.