Heat olive oil in a large soup pot over medium-high heat. Add the sliced kielbasa and cook until browned, about 5–6 minutes. Remove and set aside.
In the same pot, sauté garlic, onions, carrots, and celery until fragrant and softened, about 2 minutes.
Pour in chicken stock and add cubed potatoes. Bring to a boil, then reduce heat and simmer for 15 minutes, or until potatoes are tender.
Return the kielbasa to the pot. Stir in heavy cream, shredded cheddar, and Parmesan cheese. Season with salt and pepper.
Cook on low for another 5–10 minutes, stirring occasionally, until the cheese is melted and the soup reaches a creamy consistency.
Serve hot, garnished with fresh parsley.