Tagliatelle with Chestnuts and Pancetta

3 oz pancetta (Italian unsmoked cured bacon), chopped (scant 1 cup)
1 tablespoon extra-virgin olive oil
1 small onion, finely chopped
4 garlic cloves, minced
2 tablespoons finely chopped fresh sage
8 oz bottled peeled roasted whole chestnuts, coarsely crumbled (1 1/2 cups)
8 oz dried flat egg pasta such as tagliatelle or fettuccine
2 oz finely grated Parmigiano-Reggiano (1 cup; see Tips)
2 tablespoons unsalted butter
1 tablespoon finely chopped fresh flat-leaf parsley


Cook pancetta in oil in a 12-inch heavy skillet over moderate heat, stirring frequently, until beginning to brown, 3 to 4 minutes. Add onion and cook, stirring frequently, until beginning to brown, 2 to 3 minutes. Add garlic and 1 tablespoon sage and cook, stirring, 1 minute. Stir in chestnuts and remove from heat.

Cook pasta in a 6- to 8-quart pot of boiling salted water (see Tips) according to package directions. Reserve 1 1/2 cups cooking water, then drain pasta in a colander and add to pancetta mixture in skillet. Add 1 cup reserved cooking water along with cheese and butter and cook, tossing constantly, over high heat until pasta is well coated (add more reserved water if necessary), about 1 minute. Add salt and pepper to taste and serve sprinkled with parsley and remaining tablespoon sage.