1/2 cup olive oil, plus more for drizzling
4 carrots, coarsely chopped
2 stalks celery, coarsely chopped (leaves removed and reserved)
2 red onions, coarsely chopped
3 Yukon gold potatoes, coarsely chopped
3 zucchini, coarsely chopped
1 bunch kale, center stem removed and leaves coarsely chopped
1/2 head savoy cabbage, coarsely chopped
Sofrito (see below)
3 cups water, plus more if needed
3 cups cooked cannellini beans with 2 cups of their cooking liquid
1/2 pound rustic bread, sliced 1/2 inch thick
1/2 cup grated Parmigiano-Reggiano cheese
2 tablespoons olive oil
1 cup canned San Marzano or other good-quality tomatoes, undrained and left whole
2 cloves garlic
2 sprigs fresh rosemary, about 3 inches, leaves removed and stems discarded
1/2 cup celery leaves (reserved from above)
Place a large stockpot with the oil in the oven and heat. Add the carrots, celery, and onions and cook, stirring a few times, for about 10 minutes, or until vegetables start to soften. Add the potatoes, zucchini, kale, and cabbage and cook for 10 minutes more, stirring occasionally, while you make the sofrito (directions below).
Remove the vegetables from the oven and add the water, beans with their cooking liquid, and the Sofrito. Additional water may be needed to cover vegetables. Cover and set back in the oven to cook for 30 minutes.
To assemble, place bread slices on a sheet pan and set in the oven. Cook until lightly brown on top side only; remove. Place bread slices to partially cover bottom of a terra-cotta casserole dish and ladle soup over bread. Sprinkle with Parmigiano-Reggiano and repeat layers of bread, soup, and cheese to fill dish. Place in the oven and bake for 20 minutes, or until heated through and lightly toasted on top. Remove and stir to mix well. Spoon into serving bowls and drizzle with oil. Soup may be made a day in advance, refrigerated and assembled later.
Place a small saute pan with the olive oil, tomatoes, garlic, rosemary, and celery leaves in the oven and cook for 10 minutes. Remove, let cool slightly, and place in a food processor and puree.