Cut the sausage into 1" pieces and cook them in a skillet until cooked through. Remove from the heat and set aside.
Meanwhile, combine the stock and cream in a saucepan and cook over medium heat.
Add the potatoes and kale to the soup.
When the sausage has cooled, cut the slices into "soup sized" pieces. It's really all a matter of preference, but the smaller you cut them, the more sausage it seems like there is. Add the sausage to the soup.
Let the soup simmer until the potatoes are soft, stirring occasionally.