Heat 1 tablespoon oil in a large saucepan over medium heat. Add the onion and sauté about 2 to 3 minutes until softened.
Add the sausage and cook, breaking apart, until no longer pink, about 3 to 4 minutes.
Add the garlic and kale to the pan and cook, stirring until the kale wilts, about 2 minutes.
Stir in the tomatoes; bring to a simmer. Reduce the heat and simmer, covered, until the kale is tender, about 4 to 5 minutes.
Stir the beans into the stew and cook until warmed through, about 5 minutes.
For a thicker consistency, mash some of the beans with a fork.
Taste, add salt and pepper if necessary, and serve.