If using, simmer the chicken carcass in 6 cups of water for 30 minutes to make a quick stock. Strain and set aside.
In a large Dutch oven, melt butter with olive oil over medium heat. Add diced onion and cook until soft and translucent.
Add sliced cremini mushrooms (and rehydrated porcini mushrooms if using). Sauté without overcrowding until they brown deeply and release their moisture.
Stir in minced garlic and cook for 1 minute until fragrant.
Sprinkle the flour over the mushroom mixture and cook for 1 minute, stirring constantly.
Slowly pour in the chicken stock, whisking constantly to prevent lumps from forming.
Add the fresh thyme, bay leaves, and the shredded rotisserie chicken. Bring to a simmer.
Reduce heat to low. Temper the cream by ladling a small amount of hot broth into it, then slowly pour the mixture back into the pot, stirring constantly.
Let the soup simmer gently for 15-20 minutes, avoiding a boil. Season generously with salt and pepper to taste.
Remove the bay leaves and thyme sprigs. Serve hot, garnished with fresh parsley.
