stand mixer with pasta attachment or hand-cranked pasta machine
Bring a large pot of generously salted water to a rapid boil.
Divide the Fresh Pasta dough in half, working with one half at a time and keeping the other piece wrapped. Set up a pasta roller attachment on a stand mixer (or secure a hand roller to the side of your work surface). Lightly flour your work surface and roll out the dough until it is thin enough to pass through the pasta roller. Set your pasta roller to the widest setting. Turn on the pasta roller and pass the dough through once. Fold the rolled-out piece of dough over itself, and then pass through the roller again. If the edges begin to fray or the dough gets sticky or damp, lightly dust both sides with flour. Repeat six or seven more times, until the dough is smooth.
Adjust the roller to the second widest setting, dust both sides of the dough with flour, and pass it through twice (without folding). Repeat, adjusting to a thinner setting each time and passing through twice, until the dough is thin but not so much that it is translucent.
Dust a work surface with some semolina flour to keep the dough from sticking. Trim the dough into 10- to 12-inch long sheets, stacking them with semolina between each sheet. Fold the stack of dough sheet in half, and then in half again. Use a sharp knife to slice the dough along the short side of the stack into 1/4-inch thick slices. Unroll the noodles and toss with semolina flour to prevent sticking. Repeat the rolling and cutting process with the remaining dough.
Drop the pasta into the boiling water and stir immediately. Leave the pasta to cook, stirring occasionally, for 2 minutes. Add the green beans cook 1 1/2 minutes more. Lift the pasta and green beans from the water with tongs or a spider and place in a heatproof bowl along with about 1/4 cup pasta water. Pour about 3/4 cup pesto over the pasta and beans and toss well, adding more pesto if necessary. Top with more grated cheese.
Mound the flour in the center of a clean countertop or cutting board. Make a well in the center of the flour 3 to 4 inches wide.
Crack the eggs into the well and add a pinch of salt. Using a fork, break the yolks and begin to beat the eggs as you would if making scrambled eggs.
Continue stirring the eggs with a fork in large circles, slowly incorporating the flour. When the eggs form a thick mass and become difficult to stir, about 3 minutes, fold the loose flour from the edges into the pile with a bench scraper and knead until a smooth dough forms. Discard any excess flour.
Shape the dough into a flat disk, wrap tightly with plastic wrap and set aside to rest for 20 minutes before rolling. If waiting more than 1 hour, refrigerate or freeze the dough. The dough will keep refrigerated for up to 24 hours.
Yield: about 1 1/2 cups.
Combine the basil, spinach, garlic and a pinch of salt in a food processor or blender and pulse until finely chopped. With the machine running, stream in the oil through the opening. Add the cheese and process until almost smooth. (Add more oil if needed to create a smooth, spoonable consistency.) Taste and season with salt and pepper; transfer to a bowl.
If you don't have semolina, you can use 10 ounces of only "00" or all-purpose flour instead of 7 ounces flour and 3 ounces of semolina flour.