Remove cooked vegetables from pot (discard bay leaves) and chop roughly. Shred beef with your hands. Combine vegetables and beef in a bowl and set aside. Using a fine sieve, strain leftover sauce from pot into a second bowl. Add any remaining solids from sauce to vegetables and beef. (Meat-and-vegetable mix should now have a dry, hashlike consistency.) Gently heat leftover sauce over medium-low setting. Whisk in butter. In a medium saute pan over high heat, cook mushrooms in olive oil. Add to sauce.
Cut your Pasta Dough into 6x6-inch squares and spread them around a board. Using your hands, make a small ball (about 3 tablespoons) of meat-and-vegetable mix and place it in the center of a pasta square. (If you’re using wonton wrappers, make it 1 tablespoon.)
Repeat with remaining squares. Dab a small amount of water along outside edges of each square and fold in half, creating a triangle. Seal edges well.
Drop finished ravioli into boiling salted water and cook 6 to 8 minutes (3 if you’re using wontons).
Using a slotted spoon, transfer cooked ravioli to warm sauce, and toss gently to coat. Serve immediately.
In a small bowl, combine eggs, yolks, oil, and salt, and set aside. Place flour into the bowl of a food processor fitted with a metal blade. With the motor on, add egg mixture; then pulse just until a stiff dough forms. Scrape dough onto floured surface and knead until dough is shiny and elastic. (Use more flour if necessary.)
Cover dough with plastic wrap or a kitchen towel and let rest at least 20 minutes. Cut dough into 4 pieces. Using a pasta machine or by hand, roll out to 1/16-inch thickness, and set aside.