Yield: 1 1/2 quarts
In a 12 to 14-inch saute pan, heat the olive oil and butter together over high heat. Add the onion and cook until soft and golden brown, about 3 minutes. Add the sausage and cook over high heat, draining the excess fat if necessary, until the sausage is very browned and somewhat crispy, about 10 minutes.
Meanwhile, bring 6 quarts of water to a boil and add 2 tablespoons salt. Drop the gramigne into the boiling water and cook for 3 minutes. Drain the pasta, reserving the cooking water, and add the pasta to the sausage mixture. Toss over high heat 1 minute to coat, adding a splash of the reserved pasta water if necessary to keep the condiment from getting too "tight". Divide equally among 6 warmed pasta bowls, top with grated Parmigiano-Reggiano, and serve immediately.
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 six 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.