Preheat your oven to 375°F (190°C). Prepare your baking dish for the casserole.

Season the chicken breasts with salt and pepper, then cook in a skillet with oil for 6-8 minutes per side until cooked through.

Boil cubed butternut squash in salted water for 10-12 minutes until tender, then drain and cool.

In a mixing bowl, combine the cooked squash, shredded chicken, diced onion, and minced garlic.

Mix in chicken broth and heavy cream, then add shredded cheese, thyme, salt, and pepper, stirring well.

Spread the mixture evenly in a greased baking dish and top with remaining cheese and breadcrumbs.

Bake in the preheated oven for 25-30 minutes or until bubbly and golden brown.

Allow to cool for 5 minutes before serving.