In a large pot, melt butter over medium heat. Add onions, garlic, carrots, and celery. Sauté until onions become translucent.
Stir in the diced turkey, followed by the potatoes.
Pour in the chicken or turkey broth, ensuring that the ingredients are covered.
Add thyme and bay leaf. Season with salt and pepper.
Bring to a boil, then reduce the heat to low, letting it simmer for 20 minutes or until the potatoes are fork-tender.
Stir in the heavy cream and simmer for an additional 5 minutes.
Check for seasoning and adjust if necessary.
Serve hot, garnished with chopped parsley.