Preheat the oven to 400 degrees F. Poke a few holes in the sweet potatoes with a fork and then bake them for 60-90 minutes. When you can put a knife through without resistance they are done.
10 minutes after removing from the oven, peel the skins off and place potatoes in a bowl. 10 minutes later, mash the potatoes with a potato masher or your hands. Let sit for another 10-15 minutes until completely cooled.
Add egg yolks to the mashed sweet potatoes. Add flour in small doses, mixing slightly after each flour addition. Be careful not to overwork the dough, or it could become tough.
Flour your work surface and pour dough from bowl onto the surface. Form a ball shape with the dough and using a pastry scraper (or a knife) cut it into 4 even sections. Place 3 sections to the side. Roll the remaining section into a long log shape (like you did with play-doh as a child). If the dough is sticky add flour to the work surface or your hands.
Once you've rolled this section of the dough into approximately an inch in diameter, take your pastry scraper (or knife) and cut the log into 1-inch pieces. Next, take these small pieces of dough, roll them into balls (gnocchi shapes) with your hands and place them on a pan lined with parchment paper. Repeat steps 4-5 with all of the remaining dough.
To cook your gnocchi, bring salted water to a boil. Place gnocchi in water for roughly 3 minutes. The gnocchi is done cooking when they begin floating. (See recipe notes if you'd like to freeze some gnocchi to cook at a later date.)