Bring a large pot of salted water to a boil. Add the noodles and cook as the label directs. Reserve 1/2 cup cooking water, then drain. Toss with 1 tablespoon butter and season with salt and pepper.
Meanwhile, heat the remaining 2 tablespoons butter in a large skillet over medium heat. Add the onion and celery and cook, stirring occasionally, until slightly softened, about 3 minutes. Add the mushrooms, thyme, 1/2 teaspoon salt and a few grinds of pepper; cook, stirring occasionally, until the mushrooms are lightly golden, 6 to 7 minutes. Add the wine and cook until absorbed, about 1 minute. Add the heavy cream and bring to a boil. Reduce the heat to medium low and simmer, stirring occasionally, until the sauce is slightly thickened, 4 to 5 minutes.
Stir the turkey and spinach into the sauce and cook until the turkey is warmed through and the spinach is wilted, about 3 minutes. Stir in the reserved cooking water and return to a simmer. Remove from the heat and stir in 1/3 cup parmesan.
Toss the noodles with the turkey mixture. Sprinkle with the remaining parmesan.