Melt the butter and olive oil in a large pot over medium heat, then add the sliced mushrooms and cook undisturbed for 5 minutes until browned.
Add the diced onion and cook for 4 minutes until soft. Stir in the minced garlic and fresh thyme, cooking for 1 minute until fragrant.
Sprinkle the flour over the vegetables, stirring well to coat. Cook for 2 minutes to remove the raw flour taste.
Pour in the chicken broth slowly while whisking constantly. Bring to a gentle simmer and let thicken slightly for 10 minutes.
Lower the heat to medium-low. Stir in the heavy cream and shredded rotisserie chicken. Let warm through for 5 minutes without letting it boil. Serve immediately.
