Remove the skin from the whole rotisserie chicken and shred the meat into bite-sized pieces, discarding any bones. Season the shredded chicken with kosher salt and black pepper. Set aside.

In a large stockpot, heat olive oil over medium heat for about 1-2 minutes. Add the shredded chicken to the pot and warm it through for 2-3 minutes, then remove from pot.

Reduce heat to medium-low and add unsalted butter, melting completely. Add cremini mushrooms, onion, carrots, and celery, sauté for 3-4 minutes until tender.

Stir in minced garlic and dried thyme. Cook for about 1 minute until fragrant.

Whisk in all-purpose flour for about 1 minute until smooth and free of lumps.

Gradually pour in chicken stock, whisking continuously. Add bay leaf and return the chicken to the pot. Simmer for 4-5 minutes until slightly thickened.

Stir in half and half, heating for an additional 2-3 minutes on low heat. Adjust seasonings if necessary.

Remove bay leaf before serving. Garnish with parsley and serve warm with bread or biscuits.