Preheat your oven to 350°F (175°C) and lightly grease a 9x13-inch baking dish.

In a medium saucepan, combine wild rice and vegetable broth. Bring to a gentle boil, then reduce heat and simmer covered for about 45 minutes.

In a large skillet, melt butter over medium heat. Sauté onion until translucent, then add garlic and mushrooms, stirring until golden brown.

In a large mixing bowl, combine cooked wild rice, sautéed vegetables, heavy cream, thyme, half of the cheddar cheese, salt, and pepper. Mix well.

Transfer mixture into the prepared baking dish, spreading evenly. Top with remaining cheddar cheese.

Cover with foil and bake for 25 minutes, then remove foil and bake for an additional 15 minutes until golden brown.

Let the casserole rest for a few minutes before serving to set layers.