Pour flour and salt onto a clean work surface and make a well in the center. Place the eggs/yolks in this well and mix with a fork. Swirl the fork concentrically, slowly incorporating the flour into the eggs. Once it forms a dough, knead it for 10 minutes, form it into a ball, and let rest, covered, for 30-60 minutes.
At this point, cut dough into 3 equally sized pieces. One by one (keeping the other balls covered), run the pasta through the pasta maker, occasionally lightly dusting with flour. Once the dough has reached a thickness level of 4, run it through the cutter section, dust again with flour, and set aside to dry while you do the rest.
Add pasta to a pot of boiling water and cook for 1-2 minutes, continuously checking for desired doneness (we prefer al dente). Drain pasta and let dry.
While pasta is cooking, peel black garlic and cut into small pieces (note that it can be a bit sticky and difficult to cut). Then sauté the black garlic in olive oil and butter on medium heat for 5 minutes as the black garlic starts to break down and turn the sauce black.
Meanwhile, in a separate pan, saute the mushrooms and then the onion.
When pasta is cooked and ready to go, squeeze the lemon juice into the black garlic sauce, then mix in the pasta, mushrooms, and onions. Top with basil, Parmesan cheese, toasted pine nuts, and salt/pepper to taste.