There are several versions and methods for making gnocchi. Most common are potato gnocchi and ricotta gnocchi. Potato is easier, in my opinion as with ricotta you have to let the cheese drain using a cheesecloth usually over night. Typiclly, gnocchi are rolled off the edge of a fork for the extra grooves (better to catch sauce with) but when I want to make a ton and freeze for later, I tend to go the easier route without any grooves.
In a medium saucepan, place the potatoes and cover with cold salted water by 1 inch. Bring to a boil, lower the heat, and simmer, uncovered, until tender, about 10 minutes. Drain.
Using a ricer, or grate them on the large holes of a box grater....grate/rice the potato's. Place the potatoes onto a parchment-lined baking sheet in an even layer (don't pile the riced potatoes into mounds). Set aside to cool.
Transfer the potatoes to a large bowl and, using a spatula, gently mix in the flour, yolks, salt, nutmeg, and pepper until just combined and a soft dough is formed. Don't over mix the dough or the gnocchi will be unpleasantly tough and mealy.
On a well-floured work surface, turn out the potato dough, and divide into 6 equal parts. With the palms of both hands gently roll each part into a "rope" 3/4-inch in diameter. Using a sharp knife cut each "rope" on an angle into 3/4-inch-long pieces.
In a food processor, combine the basil, pine nuts, Parmesan, garlic, and salt and puree. While the motor is running, drizzle in the oil until incorporated. Season with pepper to taste. Use immediately or store in the refrigerator with a piece of plastic wrap placed right on the surface of the pesto to prevent discoloration, for up to 3 days, or freeze for up to 1 month.