1. In a large pot over medium heat, cook the smoked sausage slices until they start to brown. Remove the sausage from the pot and set aside.
2. In the same pot, add the diced onion and minced garlic, and sauté until the onion becomes translucent.
3. Add the cubed sweet potatoes, sliced celery, and frozen corn to the pot. Pour in the vegetable broth and bring to a boil.
4. Reduce the heat and simmer for about 15-20 minutes, or until the sweet potatoes are tender.
5. Add the cooked sausage back into the pot and stir in the milk or cream. Season with salt and pepper to taste.
6. Continue to cook for another 5 minutes to allow the flavors to blend together.
7. Serve hot, garnished with fresh parsley.