Dice the onion, carrot, and celery into uniform pieces roughly the same size so they cook evenly. Peel the potatoes and cut them into 1/2-inch cubes, setting them aside in a bowl of water to prevent browning. Brown the turkey sausage in a large pot over medium-high heat, breaking it apart as it cooks, about 5-7 minutes until no pink remains. Transfer the cooked sausage to a paper towel-lined plate to drain excess grease, leaving about 1 tablespoon of fat in the pot for flavor.
Add the butter to the pot with the remaining sausage drippings and let it melt over medium heat. Add the diced onion, carrot, and celery, stirring occasionally and cooking for 5-7 minutes until the vegetables are softened and fragrant—this develops the soup's flavor foundation. Sprinkle the flour over the vegetables and stir constantly for 1-2 minutes to create a paste-like roux, which will thicken the soup and add depth. I find this technique creates a more cohesive, creamy texture than adding flour later.
Gradually pour in the broth while stirring to smooth out any lumps in the roux, then add the potatoes and stir well. Season with salt, black pepper, and garlic powder. Bring the soup to a boil over medium-high heat, then reduce to low heat and simmer gently for 20-25 minutes until the potatoes are fork-tender. The potatoes will release starch into the broth, creating a naturally thicker, more satisfying texture.
Stir in the half-and-half and add back the cooked turkey sausage from Step 1, then add the kale and stir well to combine. Increase the heat to medium and simmer for another 5-8 minutes until the kale is tender and wilted. I like to add the kale at the end rather than earlier so it stays vibrant and doesn't become mushy—it maintains better texture and color this way.
Taste the soup and adjust seasoning with additional salt and pepper as needed. Ladle into bowls and serve hot. The soup will be rich and creamy with tender vegetables, hearty turkey, and nutritious greens.