Prepare the pasta dough according to the recipe and roll out to the thinnest setting on a pasta-rolling machine. Using a paring knife, cut the pasta sheets into long strands of spaghetti. Carefully hang the strands over a dowel over the back of a chair to dry.
Bring 6 quarts of water to a boil over high heat and add 2 tablespoons salt.
Meanwhile, in a large, heavy-bottomed skillet, heat the olive oil over medium-high heat and add the garlic. Cook for 2 minutes, until it is fragrant and golden, then add the snails and mint, and toss well. Season with salt and pepper and then add the oregano. Reduce the heat to medium-low and cook for 10 to 12 minutes.
Once the snails are cooked through and fragrant, cook the spaghetti in the boiling water until tender yet al dente, about 4 minutes. Drain, reserving a little pasta water, and add to the pan with the snails. Gently toss over high heat for 1 minute, adding more olive oil or a little pasta cooking water if necessary, and divide evenly among 6 warmed pasta bowls.
Mound the flour in the center of a large wooden cutting board. Make a well in the middle of the flour and add water. Using a fork, begin to incorporate the flour, starting with the inner rim of the well.
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.
Recipe copyright Mario Batali, 2002. All Rights Reserved.