Melt butter in the same pot. Add onions, and celery. Sauté until vegetables are softened. Stir in garlic, thyme, and mushrooms. 

Cook until mushrooms release their liquid and it evaporates, about 5 minutes.

Sprinkle flour over the vegetables. Stir well and cook for 1-2 minutes until flour smells toasty and coats the veggies.

Gradually pour in chicken stock, stirring constantly to prevent lumps. Add bay leaf and browned chicken. 

Bring to a boil, then reduce heat and simmer, covered, until chicken is cooked through and vegetables are tender.

Remove the bay leaf. Stir in cream and heat through. 

Taste and adjust seasoning with salt and pepper. If the soup is too thick, thin with more stock.

Ladle hot soup into serving bowls. Garnish with a sprinkle of chopped parsley. Serve immediately.