Heat oven to 400° F.
Peel potato and cut it into 1/2-inch pieces. Cook in salted boiling water until tender, about 15 minutes; drain. In a large bowl, whisk together eggs, milk, scallions, Parmesan, fresh parsley, and salt. Melt butter over medium heat in an 8-inch oven-proof nonstick skillet. Add the egg mixture and cook, stirring occasionally, until it begins to set, 4 to 5 minutes. Chop pork cutlets, then add the meat and potato to the egg mixture; stir. Place skillet in oven. Bake until puffed in the center and browned around the edges, about 20 minutes.