Make the pasta: Bring 3 quarts of water to a boil in a large pot and add 1 tablespoon salt. Set up an ice bath next to the stove. Blanch the spinach in the boiling water, about 2 minutes, then remove with tongs or a slotted spoon and plunge into the ice bath to cool. Drain the spinach and squeeze dry in a kitchen towel, removing as much moisture as possible. Set aside.
Combine the flour and spinach in a food processor and process until evenly green. With the motor running, add the eggs and cheese and process until the dough forms a ball around the blade. Continue to process until smooth, about 20 more seconds.
Dust a large board with flour; turn the dough out onto the board and knead a few times by hand. The dough should be elastic. Wrap in plastic wrap and let rest about 30 minutes at room temperature.
Cut the dough into 4 pieces. Wrap 3 of them in plastic wrap or cover with a slightly damp towel. Flour the board; roll out 1 piece of dough with a floured rolling pin into a 10-by-14-inch rectangle, about 1/8-inch thick. Brush the dough lightly with flour, then roll up and cut into 1/2-inch-wide strips using a sharp knife. Place the pasta in nests on a sheet tray that has been dusted with semolina flour. Cover with a clean dish towel and set aside at room temperature. Repeat with the remaining pieces of dough.
Bring a large pot of salted water to a boil. Make the sauce: Heat the olive oil in an extra-large skillet over medium heat. Scatter in the guanciale and cook until the fat is rendered and the guanciale is crisp in spots, about 3 minutes. Remove the guanciale and drain on paper towels; remove all but about 1/4 cup drippings from the skillet. Add the onion and cook until soft, 10 to 12 minutes. Return the guanciale to the skillet.
When the onion is almost soft, shake any excess flour from the pasta and add to the boiling water. Cook until al dente, stirring constantly, about 3 minutes once the water returns to a boil. Remove with tongs or a spider and add to the skillet. Add about 1 cup pasta water to the skillet and toss to coat. Remove from the heat.
In a small bowl, temper the egg yolks with 3 tablespoons warm pasta water, then pour over the pasta, tossing to make a creamy sauce. Sprinkle with the cheese and toss again, adding more pasta water as needed. Garnish with more cheese and shaved white truffle.