Yield: 4 cups
Bring 6 quarts of water to a boil and add 2 tablespoons salt.
In a 12 to 14-inch saute pan, heat the olive oil over high heat until smoking. Add the mushrooms and saute over high heat until browned, about 2 to 3 minutes per batch. The mushrooms should not release their juices. Remove the mushrooms and add the onion, leeks, garlic, thyme leaves and salt and pepper to taste. Cook for 5 more minutes, then add the tomato sauce. Bring to a boil, then reduce to a simmer and add the mushrooms. Cook 10 more minutes and set aside.
Cook the pasta in the boiling water for 1 minute. Drain, reserving the pasta water, and add the pasta to the sauce. Toss over high heat 1 minute to coat, adding a splash of pasta water if necessary to keep the sauce from getting too tight. Divide among six warmed pasta bowls and top with grated Parmigiano-Reggiano.
As you expand the well, keep pushing the flour up from the base of the mound to retain the well shape. The dough will come together when half of the flour is incorporated.
Start kneading the dough with both hands, using the palms of your hands. Once you have a cohesive mass, remove the dough from the board and scrape up and discard any leftover bits. Lightly reflour the board and continue kneading for 6 more minutes. The dough should be elastic and a little sticky. Wrap the dough in plastic and allow to rest for 30 minutes at room temperature. Roll or shape as desired.