Preheat your oven to 350°F (175°C).
In a large pot, sauté the diced onion and minced garlic over medium heat until translucent.
Add the diced butternut squash to the pot and cook for about 5 minutes, stirring occasionally.
Stir in the cooked chicken, wild rice, chicken broth, and thyme.
Pour the mixture into a greased baking dish and top with heavy cream.
Season with salt and pepper to taste, then cover the dish with aluminum foil.
Bake in the preheated oven for 40–45 minutes, then remove the foil and bake for an additional 15 minutes.
Allow the casserole to rest for 10 minutes before serving.