Brown the sausage: Heat a Dutch oven or large pot over medium-high heat. Add the turkey sausage (or your preferred option) and cook, breaking it into small pieces, until fully browned and cooked through. Drain the excess grease, leaving about 1 tablespoon in the pot for extra flavor.
Sauté the vegetables: Add butter to the pot along with the reserved sausage drippings. Stir in the diced carrots, celery, and onion, then season with salt and black pepper. Cook for 5-7 minutes, stirring occasionally, until the vegetables are soft and fragrant.
Add the flour: Sprinkle the flour evenly over the vegetables, stirring until everything is well coated.
Stir in the broth & half-and-half: Gradually pour in the chicken or vegetable broth, stirring constantly to avoid lumps. Slowly add the half-and-half, then stir in the diced potatoes.
Simmer the soup: Bring the mixture to a gentle boil, then reduce the heat to low. Let the soup simmer for 20-25 minutes, or until the potatoes are tender and easily pierced with a fork.
Final adjustments: Taste the soup and adjust the seasoning with more salt and pepper if needed. Add the cooked sausage back into the pot along with the chopped kale. Let it simmer until the kale is wilted and tender.
Serve & enjoy: Ladle the hot soup into bowls and serve with a side of ciabatta or fresh rye bread. Enjoy this comforting and hearty meal!