Heat oven to 400º F. Cook the potato in salted boiling water until tender, 10 to 12 minutes. Drain.
Meanwhile, heat the oil in a medium skillet over medium-high heat. Season the pork with ¼ teaspoon each salt and pepper.
Cook the pork until cooked through, 2 to 3 minutes per side. Cut into ½-inch pieces.
In a large bowl, whisk together the eggs, milk, scallions, Parmesan, parsley, ½ teaspoon salt, and ¼ teaspoon pepper.
Melt the butter in an 8-inch ovenproof nonstick skillet over medium heat. Add the egg mixture and cook, stirring occasionally, until it begins to set, 4 to 5 minutes.
Add the pork and potato to the skillet and stir. Place in oven and bake until the eggs are puffed in the center and browned around the edges, about 15 minutes.