Prick each sweet potato a few times with a fork. Microwave them until fork-tender, 5 to 10 minutes. Set aside until cool enough to handle, 15 to 30 minutes.
Prepare a clean working surface. Slice each sweet potato in half and use a spoon to scoop out the insides, and discard the skins. Use a potato masher to mash the insides. Measure the volume of mashed sweet potato that you have. You need 1 cup of mashed sweet potato, so discard anything more than that.
Spread out the mashed sweet potato in a thin layer on your working surface. Evenly distribute flour over the sweet potato layer. Starting at one end, use fingers to mix the sweet potato and flour to form a dough, making your way to the other end as the flour and sweet potato are incorporated into a dough ball. Do not knead any further after a dough ball is formed.
Divide the dough ball into 4 pieces. Take a piece and form a long log about 1/2 inch wide, rolling it along your working surface if it gets sticky. Cut the log into pieces about 1 inch long, which will be the individual gnocchi pieces. Optionally, use a fork to press grooves into each gnocchi. Repeat for the other 3 dough pieces. In total, you should have about 40 gnocchi pieces.
Boil water in a large pot. Add gnocchi to the boiling water. Cook until the gnocchi floats to the surface and is cooked through, a few minutes. Transfer the gnocchi to a plate and serve with sauce.