Brown the kielbasa: Melt the butter in a large pot over medium heat. Add the sliced kielbasa and cook until golden brown on both sides.
Sauté the vegetables: Add the diced onion and sliced carrots to the pot. Cook for 5–7 minutes, stirring occasionally, until softened and fragrant.
Simmer the soup: Stir in the diced potatoes and pour in the broth. Season with salt and black pepper. Bring to a boil, then reduce the heat and simmer gently for about 25 minutes, or until the potatoes are tender.
Serve: Ladle into bowls, garnish with parsley, and serve warm.