In a large Dutch oven or Soup Kettle, heat the Olive Oil over medium high heat.
Add in the sliced sausage, and cook for 5 to 6 minutes.
Remove the sausage from the Dutch oven and set to the side.
In the same pot, add in the onion, garlic, carrots and celery and cook for 2 minutes.
Add the chicken stock and add in the potatoes.
Bring to a boil and then decrease the heat to low medium, cover and cook for 15 minutes.
Add the Kielbasa back into the pot, add the milk, Parmesan Cheese and Cheddar Cheese. Season with salt and pepper.
Stir well and cook for another 10 minutes over the low medium heat until the cheese has melted.
Remove from the heat and garnish with Chopped Parsley.
Serve immediately.