Preheat oven to 350°F. Place potatoes directly on middle rack in preheated oven. Bake until very tender when pierced with a paring knife, 1 hour and 15 minutes to 1 hour and 30 minutes. Carefully cut potatoes in half lengthwise; let stand until cool enough to handle, about 20 minutes. Using a paring knife, peel potatoes, and discard skins or if using a ricer, you can rice without peeling.

Press potatoes through a potato ricer (or thoroughly mash in a bowl and then place) onto a clean work surface; spread in an even layer. Let cool until almost room temperature, about 8 minutes. Drizzle egg yolk evenly over potatoes. Sprinkle salt and 1/2 cup of the flour evenly over potatoes and egg yolk. Using a bench scraper or a rubber spatula, very gently fold mixture over onto itself several times, gradually folding in remaining 1/2 cup flour just until all flour is incorporated, and dough comes together in a mass. Do not knead or overwork.

Line a baking sheet with parchment paper, and lightly dust with flour; set aside. Clean work surface, and lightly dust with flour. Divide dough evenly into 4 pieces, about 5 1/4 ounces each. Roll 1 dough piece into a 3/4-inch-thick rope, about 9 inches long. Cut rope crosswise into 3/4-inch-long gnocchi pieces. Roll each piece against tines of a fork to make ridges, transfer to prepared baking sheet. Repeat process with remaining 3 dough pieces. Cook them now or place them of a sheet tray to freeze for another day. ENJOY!