In a skillet set over medium heat, cook the sausage until no pink remains, 5 to 7 minutes. Drain the excess grease and discard it in the trash after it cools.
Add the cooked sausage, frozen potatoes, chicken broth, pepper, and salt to the slow cooker. Set the slow cooker to high and cook until the potatoes are tender and the flavors have combined, about 3 ½ hours.
Add the chopped kale and heavy cream to the slow cooker and stir gently to combine. Continue cooking until the kale is tender, about 30 minutes.
Taste and season with more salt as desired. Serve with your favorite toppings alongside a few slices of crusty bread.
