Finely chop onion. Finely chop 2 Tbs garlic and thinly slice 1 large garlic clove, and keep 1 large garlic clove whole. Thinly slice celery. Remove kale leaves from any tough stems; discard stems and coarsely chop leaves.
Heat 3Tbs EVOO in a large pot over med-high. Add onions, celery, and chopped garlic; cook until softened, 5 min. Add 1 Tbs crushed red pepper. Add beans and their liquid, all of the broth concentrate, 3 cups water, 2 teaspoons salt, and a few grinds of pepper. Simmer, partially covered, 10 minutes.
While soup simmers, heat 1 Tbs oil in a large skillet over medium. Add sliced garlic and cook, stirring, until fragrant, about 30 seconds. Add kale and 1/4 cup water. Cook, tossing, until kale is wilted and tender, 3–5 minutes; season to taste with salt. Set sautéed kale aside.
purée soup until smooth with immersion blender. Season to taste with salt and pepper.
Thinly slice all of the mozzarella. Preheat broiler with a rack in the top position. Split each ciabatta roll, then place halves on a rimmed baking sheet and toast on both sides. Rub whole garlic clove all over cut side of toasted ciabatta.
Drizzle cut side of ciabatta toasts with oil and top with mozzarella. Broil until cheese is melted and bubbly, 1–2 minutes. Top toasts with sautéed kale. Finely grate some of the lemon zest over top of soup, along with a drizzle of oil, and a pinch of crushed red pepper, if desired.