Bring a large pot of well-salted water to a boil. Add pasta. Stir, and cook until two minutes shy of al dente. Drain, reserving at least 2 cups of pasta water.
While the pasta comes to a boil and cooks, cook the prosciutto and sage in two tablespoons olive oil over medium heat, stirring frequently, until lightly browned and crisp. Set aside on a plate.
Add the canned pumpkin purée, heavy cream, 2 teaspoons kosher salt, black pepper, and butter to the skillet. Cook, whisking, until smooth and heated through. It will be thick.
Add the drained pasta and half of the prosciutto and sage back to the skillet. Toss to coat and cook together for a minute or two, using pasta water to loosen it into a creamy sauce. (Note: I used nearly 2 cups, in several additions.)
Remove from heat. Stir in the Parmigiano-Reggiano cheese. Taste for seasoning. Spoon into pasta bowls, topping with the remaining prosciutto and sage, with a sprinkle of additional grated parmesan.
