Make the Broth (Optional but Recommended): Place the reserved rotisserie chicken carcass in a large pot. Add the onion, carrots, celery, bay leaves, and thyme. Cover with 10 cups of water. Bring to a boil, then reduce heat and simmer for at least 1 hour, or up to 3 hours. Strain the broth through a fine-mesh sieve, discarding the solids.

Sauté the Vegetables: In a large pot or Dutch oven, heat the olive oil over medium heat. Add the onion, carrots, and celery and cook until softened, about 5-7 minutes.

Add the Mushrooms and Garlic: Add the sliced mushrooms to the pot and cook until they release their moisture and begin to brown, about 8-10 minutes. Add the minced garlic and cook for another minute until fragrant.

Create the Roux: Sprinkle the flour over the vegetables and cook, stirring constantly, for 1-2 minutes.

Deglaze and Simmer: Gradually whisk in the sherry (if using) and cook for 1 minute, scraping up any browned bits from the bottom of the pot. Slowly pour in the chicken broth, whisking constantly to prevent lumps. Add the bay leaves, thyme, salt, and pepper. Bring to a simmer.

Add the Chicken: Stir in the shredded rotisserie chicken. Reduce the heat to low, cover, and simmer for at least 15 minutes, or up to 30 minutes, to allow the flavors to meld.

Finish and Serve: Remove the bay leaves. Stir in the heavy cream (if using). Taste and adjust the seasoning as needed. Garnish with fresh parsley and serve hot with lemon wedges, if desired.