For a vegan dish, you can omit the cheese and garnish with toasted pine nuts instead.
Heat 3 tablespoons oil in 12-inch nonstick skillet over medium-high heat until shimmering. Add onion and cook until softened and lightly browned, 5 to 7 minutes. Stir in kale, beans, tomatoes and their juice, and ¾ teaspoon salt. Cover and cook, stirring occasionally, until kale is very tender and sauce is thickened, 8 to 10 minutes.
Meanwhile, cook garlic, pepper flakes, and remaining 3 tablespoons oil in large saucepan over medium heat, stirring frequently, until garlic begins to turn straw-colored, about 4 minutes. Add broth and bring to boil over high heat. Whisk in polenta and remaining ¼ teaspoon salt; reduce heat to medium-low; and cook until thickened, about 3 minutes. Season with salt and pepper to taste.
Divide polenta evenly among serving bowls and top with bean mixture and mozzarella. Drizzle with extra oil and sprinkle with extra pepper flakes. Serve.
