On a clean surface, make a well in the center of the flour. Crack the eggs into the well and add 3 yolks. Gradually incorporate the flour into the eggs using a fork, blending until combined. If dry, add a 4th yolk.
Knead the dough for about 5-10 minutes until it is smooth and elastic. If the dough is too dry, add a few drops of water at a time (up to 2 tablespoons) until there are no loose crumbs. Wrap the dough in plastic wrap and let it rest at room temperature for 30 minutes.
Divide the dough into four pieces. Roll each piece into a thin sheet with a pasta machine or a rolling pin. Cut the sheets into 2-inch squares.
Place a square on a garganelli board or a ridged surface. Place a dowel at one end of the square and roll tightly to form a tube, pressing to seal the edges.
Bring a large pot of salted water to a boil. Cook the garganelli for 3 minutes or until al dente, depending on its thickness. Drain and serve with your favorite sauce.