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.
Notes
Chop the vegetables and measure the ingredients in advance to make the cooking process seamless.Adding the kale near the end helps it soften without becoming overly mushy. You don't need it to cook for long.The soup thickens slightly after refrigeration as the potatoes continue absorbing broth. If needed, add a splash of broth when reheating.