Preheat the oven to 350° Fahrenheit and grease a 9x13-inch baking dish.
Cook the spaghetti in a large pot of boiling water according to package directions until al dente, then drain and set aside.
Melt the butter in a large saucepan over medium-high heat. Add the mushrooms and onions and sauté for 5 minutes until tender. Stir in the garlic and cook for 30 seconds.
Sprinkle in the flour and cook for 1 minute while stirring continuously. Slowly pour in the chicken broth and heavy cream, stirring until smooth.
Add ½ cup each of Monterey Jack, mozzarella, and Parmesan cheese, along with the Italian seasoning, salt, and pepper. Reduce the heat to low and simmer for 5 minutes, stirring occasionally, until the cheeses melt and the sauce is creamy.
Stir in the turkey until combined, then remove the pan from heat.
Spread the cooked spaghetti in the prepared baking dish. Pour the sauce over the pasta and toss gently to coat. Sprinkle the remaining cheeses evenly over the top.
Bake for 20 to 25 minutes until the casserole is hot, bubbling, and lightly browned on top. Garnish with parsley and serve immediately.