Preheat the oven to 375 or 400 degrees F.
Bake the potatoes until they are fork tender, about 45 minutes to 1 hour. Check them!
While the potatoes are still hot peel and pass them through a food mill or ricer. (I find that the food mill works just as well as a ricer and is much easier to handle) onto a sheet tray lined with parchment paper. When doing this pay careful attention to keep the potatoes as light and fluffy as possible. This will aid in keeping the gnocchi light. Refrigerate the potatoes on the sheet tray until cold. This is also a very important step. If the potatoes are warm while adding flour they will require more flour which will result in a much heavier finished product.
When the potatoes are absolutely cold, transfer to a clean work surface. Beat together the eggs and cheese and pour onto the potatoes. Season with salt. Cover generously with flour. It should look like snow on the mountains.
Crumble the potato flour mixture between your fingers. Begin to knead the dough until it is a dry homogeneous mixture. The dough should feel slightly moist, but not tacky. If too tacky, repeat the snow on the mountains stage.
Form the dough into a large log. Cut slices off the log and begin to roll into long ropes that are about 1-inch in thickness. Cut the ropes into 1/2-inch lengths. Cover generously with flour. Place the gnocchi in a single layer on a sheet tray dusted with flour. DO NOT PILE ON TOP OF EACH OTHER!
Use or freeze the gnocchi immediately. If freezing, place tray directly into the freezer. Once frozen, the gnocchi can be stored in plastic bags, in the freezer, indefinitely. When cooking gnocchi they can go directly from the freezer into salted boiling water.
Note: It is a general practice to take gnocchi out of the water when they float. This is a big mistake. Gnocchi need to be cooked in boiling water until they float and get nice and puffy. Not cooking gnocchi long enough will also result in heavy gnocchi.