Cook the SausageHeat olive oil in a large soup pot. Add kielbasa and cook for 5-6 minutes, stirring often. Remove and set aside.
Sauté VegetablesAdd garlic, onion, carrots, and celery to the pot. Sauté for 2 minutes.
Cook the PotatoesPour in chicken stock and add potatoes. Bring to a boil, then reduce heat and simmer for 15 minutes until tender.
Add Cream and CheeseStir in milk (or cream), cheddar cheese, Parmesan cheese, salt, and pepper. Add the cooked kielbasa. Cook on low for 5-10 minutes until creamy.
Garnish and ServeStir in parsley just before serving. Ladle into bowls and enjoy warm.