In a Dutch oven or large pot over medium-high heat, add the sausage and cook, stirring and breaking up the meat with a wooden spoon, until browned, about 10 minutes.
Add the onions and garlic and cook, stirring, for another 2 to 3 minutes.
Add the potatoes and pour in the chicken broth and water. Bring to a boil over medium-high heat.
Add the kale and season to taste with salt and black pepper. Reduce the heat to low and simmer, covered, for about a half hour. Adjust the seasonings if needed.