Increase heat to medium and add Italian sausage and onion and cook, breaking up sausage, for 6-8 minutes or until onions are translucent and sausage is cooked through.
Add garlic and cook for 1-2 minutes or until fragrant, stirring constantly. Add broth, water, and potatoes and increase heat to high to bring to a boil.
Reduce to a simmer (medium-low heat) and cook uncovered for 15 minutes or until potatoes are fork tender. When potatoes are done or almost done, add kale and cook until kale leaves are tender.