Preheat oven to 425 degrees F.
Prick each potato several times with a fork, then place on baking sheet. Cook for about 1 hour. Remove from oven, let cool for 10-12 minutes until cool enough to handle.
Bring a large pot of water to a boil. Once the water is boiling add 1 teaspoon salt. Meanwhile cut each potato open lengthwise; scoop out the flesh and place through a ricer, into a bowl.
Stir in salt, Parmigiano, yolks and 1 cup of flour, just enough to combine to avoid overworking the dough (otherwise gnocchi will become tough).
Roll out into 12 x 3/4 inch snake-like shape; sprinkle with flour to avoid sticking. Cut the ropes into 3/4 inch pieces. Press each piece lightly with the tines of a fork.
In three batches, drop the gnocchi in the boiling water and let cook until the pieces all float, about 1 to 2 minutes.
Remove the gnocchi with a perforated spoon or skimmer and serve immediately.