1. To prepare pasta, lightly spoon flour into dry measuring cups; level with a knife. Combine flour and dash of salt in a food processor. Combine 6 tablespoons water, 1 1/2 tablespoons extravirgin olive oil, and egg yolks in a bowl, stirring well with a whisk. With processor on, slowly pour water mixture through food chute, processing just until dough forms a ball. Turn dough out onto a lightly floured surface; knead lightly 5 times. Shape dough into a disk. Dust dough lightly with flour; wrap in plastic wrap. Let stand 30 minutes.
2. Pat dough into a 3 x 8–inch rectangle 1-inch thick. Divide dough into 8 equal portions. Working with 1 portion at a time (cover remaining dough to prevent drying), divide dough into 14 equal pieces. Roll each piece between your palms back and forth, into a strand about 2 inches long. Place strands on a well-floured jelly-roll pan. Repeat procedure with remaining dough portions to form 112 strands.
3. Bring 6 quarts water to a boil in a large Dutch oven. Place pasta in a sieve, and shake off excess flour. Add pasta to pan. Cook for 1 1/2 minutes or until done; drain.
4. To prepare sauce, bring broth to a boil in a medium saucepan. Add morel mushrooms to pan. Remove from heat. Cover and let stand 40 minutes. Drain morel mushrooms through a colander over a bowl, reserving morel mushrooms and liquid. Halve morel mushrooms lengthwise; set aside.
5. Heat 1 1/2 teaspoons olive oil in a large nonstick skillet over medium-high heat. Add onion to pan, and sauté for 3 minutes, stirring frequently. Clear a spot in bottom of pan. Add garlic to clear spot in pan, and saute for 30 seconds. Add salt, thyme, and pepper; sauté 30 seconds, stirring frequently. Add reserved morel mushrooms and cremini mushrooms to pan. Cover, reduce heat, and cook for 4 minutes. Uncover, increase heat to medium-high, and cook 2 minutes or until liquid almost evaporates, stirring frequently. Clear a spot in bottom of pan. Add tomato paste to clear spot; cook 1 minute. Stir tomato paste into mushroom mixture.
6. Stir in 1 cup reserved mushroom liquid. Cook for 8 minutes or until very thick, stirring occasionally. Stir in remaining mushroom liquid; cook for 4 minutes or until slightly thick, stirring occasionally. Add pasta and parsley to sauce mixture; toss well. Stir in truffle oil. Serve with cheese.