In a large pot, heat olive oil over medium heat. Add the chicken or turkey sausage, breaking it apart with a spoon. Cook until browned and no longer pink. Remove the sausage from the pot and set aside.
Add the chicken broth and sliced potatoes to the pot. Bring to a boil, then reduce the heat to simmer. Cover and cook until the potatoes are tender, about 10-15 minutes.
Stir in the heavy cream and chopped kale. Cook until the kale is wilted and the soup is heated through, about 5 minutes.
Return the cooked sausage to the pot. Season the soup with salt, pepper, and crushed red pepper flakes (if using) to taste. Let the soup simmer for another 2-3 minutes to blend the flavors. Serve hot.