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Heat the oil in a large pot over medium high heat on the stove.
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Saute the sausage until browned and cooked through. Remove and set aside.
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Add the onions, celery, carrots and garlic to the pot, and saute until becoming tender.
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Pour in the chicken broth and add the potatoes to the pot. Bring to a boil, cover and simmer until the potatoes are tender. This takes about 15 minutes.
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Return the sausage to the pot along with the milk, cheddar cheese and parmesan cheese. Simmer for another 10 minutes.
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Add salt and pepper to taste, and serve immediately garnished with chopped parsley.
