Heat olive oil in a large soup pot or Dutch oven over medium-high heat. Add the kielbasa and cook, stirring frequently, for 5–6 minutes, or until browned. Once done, use a slotted spoon to remove the kielbasa and set it aside.
In the same pot, sauté the garlic, onions, carrots, and celery for about 2 minutes, or until fragrant.
Pour in the chicken stock and add the potatoes. Bring the mixture to a boil, then reduce the heat, cover, and let it simmer for 15 minutes, or until the potatoes are tender.
Return the browned kielbasa to the pot. Stir in the milk, cheddar cheese, Parmesan, salt, and pepper. Continue cooking over low heat for 5–10 minutes, stirring occasionally, until the cheese melts and the soup becomes creamy.
Just before serving, garnish with fresh parsley. Enjoy!