Heat oil in a large soup pot or Dutch oven over medium heat. Add shallot or onion and carrots then saute until crisp tender, 5-7 minutes, placing a lid on top for the last few minutes to help speed along the softening process. Turn heat up slightly then add kielbasa and continuing sauting until sausage starts turning golden brown, 5 minutes. Add garlic then saute until extremely fragrant and golden brown, 1-2 minutes, being careful not to burn the garlic.

Add a glug of chicken broth then use a spatula or wooden spoon to scrape up the caramelized bits from the bottom of the pot. Add remaining chicken broth plus beans, bay leaf, and parmesan cheese rind then turn heat up to high to bring soup to a bubble. Turn heat down to medium-low then simmer for 15 minutes.

Add fresh spinach and grated parmesan cheese then stir and simmer until spinach is wilted, 1-2 minutes. Remove bay leaves (you can leave parmesan cheese rind in to continue to flavor the soup) then scoop into bowls and serve.