12 ounces fresh or dried tagliatelle Coarse salt and freshly ground pepper
3/4 pound boneless, skinless chicken thighs
2 tablespoons unsalted butter
2 shallots, halved, peeled, and thinly sliced (about 1/2 cup)
8 ounces cremini mushrooms, halved (or quartered if large)
1/2 cup dry white wine
3/4 cup heavy cream
1 ounce Parmesan, grated (about 1/3 cup), plus more for serving
1 stalk celery with leaves, cut into very thin slices (about 2/3 cup)
1/3 cup coarsely chopped fresh flat-leaf parsley leaves
1. Cook pasta in a large pot of generously salted water until al dente. Reserve 1 1/2 cups pasta water; drain.
2. Season chicken with salt and pepper. Melt 1 tablespoon butter in a large skillet over medium-high heat. Brown chicken, flipping once, until cooked through, 6 to 8 minutes; transfer to a plate. Reduce heat to medium; melt remaining 1 tablespoon butter. Cook shallots and mushrooms, stirring, until golden brown, about 8 minutes. (If skillet browns too quickly, add a little pasta water.) Add wine, bring to a boil, and reduce by half. Slice chicken; add to pan with cream, Parmesan, 1 cup pasta water, and pasta. Toss until sauce coats pasta, adding more pasta water if needed. Add celery and parsley; toss to combine. Serve with Parmesan.