Bring 3 cups water to a boil in a large Dutch oven; add kale. Cook 6 minutes or until tender; drain in a colander over a bowl, reserving 1 cup cooking liquid.
Heat oil in a large nonstick skillet over medium-high heat. Add the onion and oregano; sauté 5 minutes. Add tomato, salt, crushed red pepper, and minced garlic; saute 1 minute. Stir in kale, reserved liquid, and beans; cook 3 minutes.
Rub garlic halves on 1 side of each toast slice. Place toast slices, garlic sides up, on 4 plates; sprinkle each slice with 2 tablespoons cheese. Top each with 1 cup bean mixture and 1 tablespoon cheese.