Heat olive oil in a Dutch oven or large soup pot over medium-high heat. Add the sausage and cook for 5-6 minutes, stirring often. Use a slotted spoon to remove the sausage and set it aside.
Add the garlic, onions, carrots, and celery to the pot. Sauté for 2 minutes.
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 about 15 minutes, or until the potatoes are tender.
Return the cooked sausage to the pot, and add the milk, cheddar cheese, Parmesan cheese, salt, and pepper. Stir and cook over low heat for 5-10 minutes, until the cheese is fully melted and incorporated.
Stir in the chopped parsley just before serving. Enjoy!
