In a large saucepan, heat 1 1/2 tablespoons oil over medium heat. Add onions and cook, stirrring constantly, until golden, about 5 minutes.
Add garlic and cook, stirring occasionally, until fragrant, about 1 minute. Add potatoes and cook, stirring frequently, 5 minutes longer (of using left over cooked potatoes omit this step). Stir in chicken broth and 1 cup water and bring to a boil. Reduce heat to medium-low, cover and simmer until potatoes are softened, about 15 minutes.
In a large non-stick skillet, heat remaining 1/2 tablespoon oil over medium heat. Add sausage and cook, turning occasionally, until golden, 6 to 8 minutes. Remove sausage to paper towels to drain.
With a potato masher, mash potatoes directly in saucepan. (If using left over potatoes add them now and mash). Add sausage, salt, and pepper and bring to a boil. Reduce heat to low, and simmer about 5 minutes. Add kale and simmer until tender, about 5 to 8 minutes longer.