Place the potatoes in a large pot and cover with cold water. Cover and bring to a boil. Reduce to a low boil and cook until the potatoes are completely tender, 20-30 minutes.
Preheat oven to 300˚F (150˚C).
Gently remove the tender potatoes from the water and arrange in a single layer on a baking sheet. Place in the preheated oven and cook for about 5 minutes or just until all the moisture is removed from the outside of the potatoes.
Remove from the oven and set aside just until cool enough to handle. Peel the warm potatoes and mash until completely smooth in a large bowl or press through a potato ricer. Make sure there are no lumps.
Mix the flour, cornstarch, salt, nutmeg, pepper, and egg yolks into the smooth mashed potatoes just until combined.
On a lightly floured surface, gently knead the dough just until smooth. Only add more flour as necessary to keep the dough from sticking to your hands.
Dust two baking sheets lightly with flour.
Divide the dough into four equal pieces. Roll one piece into a long rope about 1/2 inch (1.25 cm) thick. Cut the rope into 1 inch (2.5 cm) pieces.
Roll one piece gently between your hands to form a finger shape with tapered ends. Place on the flour-dusted baking sheet and repeat with the remaining pieces, then the remaining dough.
Bring a large pot of salted water to a boil. Reduce to a simmer and add the Schupfnudeln in batches, being careful not to overcrowd. Cook just until they rise to the surface. Remove with a slotted spoon to a plate and set aside. Repeat with the remaining pieces.
Place 2 tablespoons (30 grams) butter in a large skillet over medium heat. Once heated and the butter is melted, add the boiled Schupfnudeln in batches in a single layer, taking care not to overcrowd. Cook until golden brown on each side, about 5 minutes. Add more butter as needed to additional batches.
Serve hot with parsley if desired.