Preheat oven to 350°F (175°C). Grease a 9x13-inch baking dish.
Cook angel hair pasta according to package directions until al dente. Drain and set aside.
In a large skillet over medium heat, melt butter. Add garlic and sauté until fragrant, about 1 minute.
Stir in cream of chicken soup, cream of mushroom soup, cream cheese, chicken broth, white wine (or additional broth), Italian seasoning mix, and black pepper. Stir until smooth and creamy.
Add cooked chicken to the sauce and stir to coat.
Toss pasta with sauce and chicken mixture until evenly combined.
Transfer mixture into prepared baking dish. Top with mozzarella and Parmesan cheese.
Bake uncovered for 25–30 minutes, until casserole is bubbly and cheese is melted.
Garnish with fresh parsley before serving.