Add olive oil to a Dutch oven or soup pot and heat over medium-high heat. Add the sausage and cook for 5-6 minutes, stirring frequently. Remove the sausage using a slotted spoon.
Add garlic, onions, carrots, and celery and sauté for 2 minutes.
Add the chicken stock and potatoes. Bring to boil and then reduce heat. Cover and cook for 15 minutes, or until the potatoes are tender.
Add the cooked sausage, milk, cheddar cheese, parmesan cheese, salt, and pepper. Stir and cook on low heat 5-10 minutes longer, until the cheese has melted.
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