Preheat the oven to 375°F (190°C).
In a large skillet, melt the butter over medium heat. Add the diced onion and sliced mushrooms, and sauté until softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the vegetables and stir well to coat. Cook for 1-2 minutes to remove the raw flour taste.
Gradually whisk in the milk and chicken broth, stirring constantly to avoid lumps.
Cook the sauce until it thickens, about 5 minutes. Stir in salt, black pepper, dried thyme, and paprika.
Remove the sauce from heat and stir in 1 cup of shredded cheddar cheese until melted and smooth.
In a large mixing bowl, combine the shredded rotisserie chicken, cooked elbow macaroni, thawed peas, and the cheese sauce. Mix well to combine.
Transfer the mixture to a greased 9×13 inch casserole dish and spread evenly.
Sprinkle the remaining 1/2 cup cheddar cheese, grated Parmesan cheese, and breadcrumbs evenly over the top.
Bake uncovered in the preheated oven for 30-35 minutes or until the casserole is bubbly and the topping is golden brown.
Remove from the oven and let rest for 5 minutes before serving.