Set potatoes on a wire rack set over a baking sheet. Bake until completely tender throughout when pierced with a fork, about 45 minutes.
Transfer potatoes to a work surface. Slice each in half lengthwise. Scoop potato flesh into a ricer or food mill fitted with the finest disk.
Add beaten egg yolks to potato mix. Scoop 1 cup flour into a fine-mesh sieve and tap to dust flour all over potatoes.
Add Parmesan and remaining flour.
Knead dough until a uniform ball is formed. Do not over mix.
Using a bench scraper, slice off a roughly 2-inch-thick portion of dough and roll into a snake about 1/2-inch-thick; Use a light touch as you roll.
Slice dough snake into 1” pieces.
Flour the gnocchi after they have been cut and then either freeze them or cook them right away.