Melt butter in a large, heavy saucepan over medium heat. Add mushrooms, onion, and garlic. Cook, stirring often until tender, about 10 minutes.

Add salt, pepper, and thyme. Stir in chicken broth, heavy cream, and cream cheese.

Reduce heat to a low simmer. Add sherry and continue to cook, stirring constantly, until cream cheese is incorporated, about 45 minutes.