Heat the oil in a large saucepan or Dutch oven over medium heat. Add the sausage and cook, stirring once, until browned, 2 to 3 minutes.
Stir in the garlic and cook for 2 minutes more.
Add the beans, broth, and tomatoes and their liquid and bring to a boil.
Add the kale and ¼ teaspoon each salt and pepper. Simmer, stirring occasionally, until wilted, 2 to 3 minutes. Serve with the bread, if using.