**Sauté the Vegetables:** In a large pot or Dutch oven, melt butter over medium heat. Add onion, carrots, and celery. Cook until softened, about 5 minutes. Stir in garlic and cook for an additional minute.

**Make the Broth Base:** Sprinkle flour over the vegetables and stir well to coat. Cook for 1-2 minutes to eliminate the raw flour taste. Gradually whisk in the chicken broth until smooth.

**Add Chicken and Seasonings:** Stir in shredded chicken, thyme, parsley, black pepper, and salt. Bring the mixture to a boil, then reduce the heat to a simmer.

**Prepare the Biscuits:** Separate the biscuit dough and cut each biscuit into quarters. Roll the pieces slightly to form dumpling shapes if desired.

**Cook the Dumplings:** Drop the biscuit pieces into the simmering soup. Cover the pot with a lid and let the dumplings cook for 10-12 minutes, stirring occasionally, until they are puffed up and cooked through.

**Finish with Cream:** Stir in the heavy cream and let the soup heat through for 2-3 minutes. Taste and adjust seasoning if needed.

**Serve:** Ladle into bowls and garnish with fresh parsley, if desired.