Preheat an oven to 350°F (175°C). Place the rotisserie chicken in a roasting pan and bake for 15–20 minutes. Let it cool slightly, then remove the meat from the bones; shred the chicken into bite-size pieces and set aside.
In a large pot or Dutch oven, heat the butter (or olive oil) over medium heat. Add the onion, celery, and carrots, and sauté for 5 minutes, or until tender.
Add the garlic and thyme, stir for 1 minute, then add the bay leaf. Pour in the chicken stock and bring to a simmer.
Add the uncooked wild rice and long-grain rice (or brown rice) and stir to combine. Reduce heat to low, cover, and simmer for 35–40 minutes, or until both rices are cooked through and tender.
Stir in the shredded chicken, heavy cream (or coconut milk), and freshly ground pepper. Simmer for another 10 minutes, but do not let the mixture boil after adding the cream to avoid curdling.
Taste and adjust the seasoning with salt and pepper. Remove the bay leaf. Garnish with fresh parsley before serving.