Preheat your oven to 350°F and lightly grease a 9x13 inch baking dish. Cook the linguine according to package directions until al dente, then drain and set aside.
Melt the butter in a large skillet over medium heat. Add the mushrooms and onion, sautéing until the onions are translucent and the mushrooms have released their liquid, about 8 minutes. Stir in the garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the mushroom mixture and cook, stirring constantly, for 2 minutes to form a light golden paste. Slowly whisk in the chicken broth, followed by the heavy cream and white wine, until the sauce is smooth and begins to thicken, about 5 minutes.
Remove the skillet from heat and stir in the cooked chicken, peas, 1/2 cup Parmesan cheese, nutmeg, and a generous amount of salt and pepper. Gently fold in the cooked pasta until everything is evenly coated in the creamy sauce.
Transfer the mixture to the prepared baking dish and top with an additional sprinkle of Parmesan. Bake uncovered for 25-30 minutes, until the top is lightly golden and the sauce is bubbling around the edges. Let rest for 5 minutes, then garnish with fresh parsley before serving.