Place potatoes into a large stockpot of cold water with skins on. Bring to a boil and cook until just soft enough to pierce with a knife.
As soon as possible after removing from water, peel the potatoes. You can try using a peeler, but it’s easier just to carefully pull the skins off with your fingers. The skin will easily peel away.
Immediately run the potatoes through the ricer and lay out in an even layer to cool. Getting the potatoes riced while they are still hot will allow the most steam to escape = drier potatoes = better gnocchi.
Beat the egg and salt in a small bowl.
Gently form the cool potatoes into a mound and make a well in the center. Pour the egg mixture into the well and gently mix together with both hands. Add the cheese and then gradually add flour to form the dough. You probably will not need all of the flour. The dough should be smooth and sticky. Be careful not to overwork the dough – if you add flour too gradually and knead the dough too much, it will become overworked and heavy.
Cut the dough into 6 pieces. Using the palms of your hands with your fingers flexed backward, gently roll the each piece of dough into a rope. Slice each rope into ½ inch pieces.
The next part is tricky. Hold a fork with tines perpendicular to the countertop. Use your thumb to gently roll the pieces of dough down the fork tines. This will make those nice grooves in the dumplings. If you can’t get the hang of it, don’t worry about it. Just make a dimple with your thumb and be done with it.
Place the dumplings on a floured kitchen towel as you go. Once you finish making all the dumplings, you will need to cook the gnocchi right away or freeze it.
Bring a pot of salted water to a boil. Drop gnocchi into the pot. When they float, they are done.
While the gnocchi are boiling, melt a tablespoon or two of butter in a skillet over medium heat. Scoop the floating gnocchi out of the boiling water with a spider or slotted spoon and add them to the butter to brown very slightly.
Warm your fresh or frozen peas using a method of your liking.
To sauce the gnocchi, add the pesto to a large mixing bowl, add the browned gnocchi and stir to coat, mix in the peas and serve.