Roll the pasta out to the #4 setting, and form into gramigne. To form into gramigne, cut the dough into fingers that are 1/2-inch thick and 3 inches long. Starting with the palm of your hand, roll the dough pieces lengthwise. It should look like a piece of squiggly spaghetti.
In a 12 to 14-inch saute pan, heat the olive oil and butter together over high heat. Add the onion and garlic 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 (don't stir too much) about 10 minutes.
Add the wine and, stirring frequently, allow it to evaporate almost completely. Stir in the milk, chicken stock, tomato paste, herbs and salt and pepper, to taste, and reduce heat to a simmer. Cook for 15 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.
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