Cook the Sausage
Heat the olive oil in a large pot over medium heat. Add the Italian sausage, breaking it into bite-sized pieces with a spatula. Cook until browned and fully cooked, approximately 6 minutes. Remove the sausage using a slotted spoon and set aside, leaving the rendered oil in the pot.
Prepare the Aromatics
Into the same pot, add the chopped onion, celery, and garlic. Sauté until the onion becomes translucent, around 4 minutes. Sprinkle in the flour, stirring continuously until it forms a light coating over the vegetables, about 1 minute.
Incorporate the Broth
Gradually pour in the chicken broth while stirring, scraping the bottom of the pot to deglaze. Bring the mixture to a simmer.
Add Potatoes and Beans
Stir in the diced potatoes and cannellini beans. Reduce the heat to low, cover the pot, and allow the soup to simmer for about 15 minutes, or until the potatoes are tender.
Finish with Kale and Cream
Add the chopped kale to the soup, cooking for 4 to 5 minutes until softened. Remove the pot from heat and let the soup cool slightly before stirring in the heavy cream or half-and-half. Return the cooked sausage to the soup and mix well.
Season and Serve
Taste the soup and adjust with salt and freshly ground black pepper as needed. Serve hot, and enjoy.
Storage
Store in an airtight container in the refrigerator for up to 5 days. Reheat in the microwave or on the stovetop over low heat until thoroughly warmed.