PREHEAT the oven to 400 degrees . Line a baking sheet with foil. Scrub the potatoes; poke all over with a fork. Place on the sheet and bake until fork-tender, about 1 hour. Slice in half lengthwise; let sit on the baking sheet until cool enough to handle.
SCOOP out the potato flesh with a spoon. Working in batches, press through a ricer into a medium bowl.
MEASURE out 3 cups of potatoes by gently scooping the measuring cup into the bowl. Dump onto a work surface in a thin layer; let cool. Meanwhile, bring a large pot of salted water to a boil.
SPRINKLE the potatoes with 1/2 tsp. salt and the nutmeg; drizzle with the egg yolks. Dust with 1/2 cup flour. Using a bench scraper, gently fold in the yolks and flour.
DUST the dough with 1/4 cup flour. Lift, fold and press with the scraper until most of the flour is mixed in. Press the dough together in a ball; set aside. Scrape the surface clean; dust with flour. Clean off the bench scraper.
FOLD and knead the dough with your hands on the work surface for just 2 turns.
SPRINKLE a baking sheet with flour. Quarter the dough. Roll one-quarter of the dough into a long, 3/4-inch-wide rope. Using the bench scraper, cut into 1-inch pieces; place on the baking sheet. Repeat with the remaining dough.
COOK the gnocchi in gently boiling water until they float to the surface and puff up slightly, about 11/2 minutes. Meanwhile, melt the butter in a large nonstick skillet
SCOOP the gnocchi into the skillet using a slotted spoon. Add 1/4 cup cooking water and the cheese. Toss to combine, adding more cooking water if too dry. Sprinkle with more cheese and the parsley