Preheat the oven to 400°F. Grease a 13x9-inch baking dish with unsalted butter.
Bring a large pot of salted water to a boil. Add the pasta and cook until al dente, about 10 minutes. Drain the pasta and set it aside.
In a large heavy-bottomed stock pot or Dutch oven set over medium-low heat, add the butter, mushrooms, onion, garlic, thyme and 1/2 teaspoon kosher salt. Cook, stirring occasionally, for 5 minutes.
Sprinkle the flour over the vegetables and cook, stirring constantly, for 2 minutes.
Stir in the chicken stock and heavy cream, scraping up any brown bits from the bottom of the pot. Bring the mixture to a boil then reduce it to a simmer and cook until the mixture has thickened slightly, about 3 minutes.
Stir in the white cheddar cheese, shredded turkey and peas then taste and season the mixture with salt and pepper.
Stir in the cooked pasta then transfer the mixture to the baking dish. Sprinkle the breadcrumbs on top then bake until the breadcrumbs are golden brown and the mixture is bubbling, 20 to 25 minutes.
Remove from the oven and let cool for 10 minutes before serving.