Place potatoes in a large pot. Add water to cover by 1"; bring to a boil, reduce heat to medium, and simmer until tender, 25–30 minutes. Drain; set aside and let cool slightly. Peel potatoes. Pass through ricer or a food mill or sieve, into a large bowl. Whisk egg and egg yolk in a small bowl to blend. Add egg mixture, 1/3 cup Parmesan, 1 cup flour, 1 teaspoon salt, and nutmeg to potatoes. Using your hands, gently mix to form a soft but not sticky dough. Transfer dough to a floured surface. Gather into a ball, then divide into 4 pieces.