Poke holes in the sweet potatoes with a fork. Then place them in a microwave safe bowl. Microwave the potatoes for about 8-10 minutes, flipping them half way through.
Line a sheet pan with paper towel. Once the sweet potatoes become fork tender, scoop out the flesh and transfer them to the sheet pan. Let the sweet potato cool down in the lined sheet pan for about 5 minutes. (The paper towel will help draw out the excess moisture from the sweet potato.)
Then rice or smash the potatoes and spread them out onto the lined sheet pan again for about 10 minutes to draw out any additional moisture.
Transfer the mashed sweet potato to a bowl. Then add the egg yolk and work the yolk into the sweet potato with a spoon or spatula. Then sift half the flour and all of the salt into the bowl. Combine everything with a spatula. Then sift the rest of the flour and combine everything again with the spatula until the dough comes together.
Flour your work surface and gently knead the dough a few times. Form the dough into a ball and lightly flour the top of the dough. TIP: It is important to not over knead the dough. Just a few gentle kneads is all that is required. If the dough is over kneaded, it will overwork the gluten which will then make the dough become sticky and gluey. Refer to my tips in the post above for further details.
Cut the dough ball into 6 equal pieces. Then roll out each piece of dough into a log that 3/4" in diameter. Then cut the log into 1-inch segments and then transfer the gnocchi onto a floured baking sheet to keep them from sticking together. Repeat until all the dough pieces have been rolled out and cut into 1" segments.
Bring a large pot of salted water to boil. Add the gnocchi and boil until the gnocchi rises to the top of the water which should take about 2 minutes. Using a slotted spoon, transfer the gnocchi to the pan to assemble the pasta.