How to Make It
Heat 2 tablespoons of the oil in a large pot or Dutch oven over medium heat. Add the leeks and garlic. Cook, stirring occasionally, until soft, 8 to 10 minutes. Add the kale and cook, stirring occasionally, until wilted, 2 to 3 minutes.
Add the broth, beans, tomatoes (and their juices), 1 teaspoon salt, and ½ teaspoon pepper and bring to a boil. Reduce heat and simmer, partially covered, stirring occasionally, until thickened, 20 to 30 minutes. Stir in the Parmesan.
Tear the toasted bread into large pieces and drizzle with 2 tablespoons of the oil.
Serve warm topped with the bread. Drizzle with the remaining 2 tablespoons of oil and sprinkle with additional Parmesan.