Melt butter over medium heat in a Dutch oven or soup pot. Add carrots, celery and onion and cook for 5 minutes, stirring frequently.
Add mushrooms and garlic. Continue to cook (stirring frequently) until mushrooms are tender (about 4 to 5 minutes).
Slowly add flour while stirring. Add broth, thyme and cooked chicken. Stir to combine.
Bring to a simmer, stirring frequently. Cover and reduce heat to maintain a simmer.
Simmer for about 15 minutes (stirring occasionally), or until vegetables are tender.
Remove from heat and stir in heavy cream, salt and pepper.
Garnish with fresh thyme sprigs when serving (if desired).