Preheat the oven to 400°F and line a baking sheet with wax or parchment paper.

Wash potatoes and pierce several times with a fork.  Microwave on high for 10 minutes.  Flip potatoes and microwave for an additional 5 minutes.  Transfer to the oven and bake for 15 minutes.  Instead of microwaving, potatoes can be baked for 1 hour.

Halve the potatoes and scoop the flesh into a ricer and rice the potatoes.  Transfer 2 slightly packed cups of riced potatoes to a bowl.  Stir in the egg yolks and 1 teaspoon of salt. Add flour and knead the dough gently until smooth but slightly sticky.

Roll 1/4 of the dough into a 3/4 inch thick rope.  Cut the ropes into 3/4 inch pieces.  Roll each piece against the tines of a fork to make the ridges; transfer to the baking sheet. Repeat with remaining dough.

In a large, deep skillet or sauce pan of simmering salted water, cook the gnocchi until they rise to the surface, then simmer for 2 more minutes.  In a large skillet, melt the butter.  Using a slotted spoon, add the gnocchi to the butter.  Season with salt and pepper and cook over high heat for 1 minute.  Sprinkle with cheese and serve.