How to Make It
Preheat the oven to 400°. Using a fork, pierce the potatoes all over and wrap them in foil. Bake the potatoes for about 1 hour, until tender; let cool slightly.
Peel the warm potatoes and pass them through a ricer into a large bowl. Using your hands, gently mix in the egg yolks. Sprinkle the flour, cheese and sea salt on top and gently stir them in with your hands. Scrape the dough onto a lightly floured surface and knead gently until smooth.
Gently roll the potato dough into 1 1/2-inch balls and transfer to a wax paper-lined baking sheet. In a large saucepan of salted simmering water, simmer half of the dumplings until they are cooked through, 7 to 8 minutes. Using a slotted spoon, transfer the dumplings to a large shallow bowl and drizzle with oil. Repeat with the remaining dumplings. Sprinkle the dumplings with chopped parsley and flaky sea salt and serve.