Add mushrooms and cook until they release their moisture and begin to brown, about 5 minutes.
Pour in chicken broth and bring to a simmer. Cook for 10 minutes.
Add heavy cream and return the chicken to the pot. Simmer for an additional 5 minutes.
Season with salt and pepper, and garnish with thyme or parsley before serving.
Notes
For a dairy-free version, use coconut milk or almond milk as a substitute for cream. You can also make this ahead and store it in the fridge for up to 3 days.