01 - Preheat the oven to 375°F. Lightly grease a 9x13-inch baking dish to prevent sticking.
02 - Cook spaghetti or fettuccine in a large pot of salted boiling water until just al dente. Drain and set aside.
03 - Melt 4 tablespoons unsalted butter in a large skillet over medium heat. Add finely chopped onion and cook until translucent, about 3 minutes. Add sliced mushrooms and cook until softened, 4 minutes more. Stir in minced garlic and sauté for 1 minute.
04 - Sprinkle all-purpose flour over the vegetables and cook, stirring constantly, for 1 to 2 minutes. Gradually whisk in chicken or turkey broth, followed by whole milk and heavy cream. Simmer gently, stirring often, until sauce thickens, about 5 minutes.
05 - Add grated Parmesan cheese, dried thyme, salt, and black pepper to the sauce. Stir until cheese is fully melted and incorporated.
06 - Remove skillet from heat. Fold in diced or shredded turkey, thawed peas, and cooked pasta until mixture is evenly coated with sauce.
07 - Spoon the turkey-pasta mixture into the prepared baking dish, spreading evenly.
08 - In a small mixing bowl, combine breadcrumbs, grated Parmesan cheese, and melted butter. Sprinkle the mixture evenly over the surface.
09 - Bake uncovered for 25 to 30 minutes, until casserole is bubbling and the topping is golden brown. Allow to stand for 5 minutes before serving.