Melt butter in a large stockpot or Dutch oven over medium heat. Add garlic and mushrooms, and cook, stirring occasionally, until tender and browned, about 5-6 minutes; season with salt and pepper, to taste. Stir in onion and cook, stirring frequently, until translucent, about 2-3 minutes.

Stir in chicken broth, heavy cream and thyme.

In a small bowl, whisk together cornstarch and 1/4 cup water. Stir in mixture to the soup until slightly thickened, about 1-2 minutes; season with salt and pepper, to taste. If the soup is too thin, add more cornstarch as needed until desired consistency is reached.