In a large soup kettle, heat olive oil over medium heat. Add uncooked ground sausage, chopped celery and chopped onion. Sauté together until meat is browned.
Add potatoes to the cooked sausage, onion and celery. Add chicken broth and water. Season with salt and pepper if desired. Bring to a boil then simmer and cover for about 10-12 minutes until potatoes are fork tender.
Add milk and stir in kale. If you like your soup to be thicker, whisk together 2 tbsp cornstarch and 2 tbsp water and pour into soup and bring to a gentle boil until it thickens. Garnish with fresh grated Parmesan cheese if desired.