Brown the sausage: In a large pot, melt 2 tablespoons of unsalted butter over medium heat. Add 1 pound of sliced kielbasa sausage, cooking for 4-5 minutes until crispy and browned. Remove the sausage from the pot and set it aside.

Sauté the vegetables: In the same pot, add 1 chopped medium onion, 3 minced garlic cloves, 2 diced carrots, and 2 chopped stalks of celery. Sauté for about 5 minutes until the onion is translucent and the carrots soften.

Create the roux: Sprinkle 2 tablespoons of all-purpose flour over the sautéed vegetables, stirring well. Cook for an additional 2 minutes.

Incorporate the broth: Gradually whisk in 4 cups of chicken broth, ensuring no lumps remain. Continue stirring until the soup thickens slightly, about 3-4 minutes.

Add the potatoes: Once the broth is smooth, add 4 diced medium potatoes. Bring to a gentle boil, then reduce to a low simmer. Cook uncovered for about 15 minutes until the potatoes are fork-tender.

Return the sausage: Stir in the browned kielbasa sausage and let it heat through for about 5 minutes.

Add cream and seasoning: Lower the heat and gently stir in 1 cup of milk, 1 cup of heavy cream, 1 teaspoon of dried thyme, and 1 teaspoon of smoked paprika. Adjust seasoning with salt and pepper.

Garnish and serve: Taste and adjust seasoning if needed. Serve hot, garnished with 2 tablespoons of freshly chopped parsley.