Boil or bake potatoes until completely tender. Rice or mash them while still hot. Let cool until just warm — not hot — on a clean surface.
Mix in flour, egg yolk, and salt. Bring together gently with your hands. The dough should just hold together without being sticky. Add flour 1 tbsp at a time if too sticky. Less flour = lighter gnocchi. More flour = dense gnocchi.
Divide dough into 6 pieces. Roll each into a ¾-inch rope on a lightly floured surface. Cut into 1-inch pieces.
Cook immediately in a large pot of heavily salted boiling water. They're done 30 seconds after they float to the surface.
While gnocchi cooks, warm butter and heavy cream in a large skillet. Stir in parmesan until melted and smooth.
Scoop gnocchi directly from the water into the sauce using a slotted spoon. Toss gently.