• 1/2 1-pound loaf sourdough bread, torn into 2" pieces (about 6 cups)
• 1 bunch collard greens, center ribs and stems removed
• 1 bunch Tuscan or other kale, center ribs and stems removed
• Kosher salt
• 1/2 cup olive oil, divided, plus more for serving
• 2 medium carrots, peeled, finely chopped
• 2 celery stalks, finely chopped
• 1 leek, white and pale-green parts only, chopped
• 4 garlic cloves, chopped
• 1/2 teaspoons crushed red pepper flakes
• 1 28-ounce can whole peeled tomatoes, drained
• 8 cups low-sodium vegetable broth
• 3 15-ounce cans cannellini (white kidney) beans, rinsed
• 4 sprigs thyme
• 1 sprig marjoram or oregano
• 1 bay leaf
• Freshly ground black pepper
• Shaved Parmesan (for serving)

Scatter bread on a rimmed baking sheet in a single layer. Let stand at room temperature to slightly dry out, about 2 hours.

Working in batches, cook collards and kale separately in a large pot of boiling salted water until slightly softened, about 3 minutes per batch. Rinse to cool. Squeeze out excess water; roughly chop. Set aside.

Heat 1/4 cup oil in a large heavy pot over medium heat. Add carrots, celery, and leek; stir often until softened, 8-10 minutes.

Add garlic and red pepper flakes. Cook, stirring until fragrant, about 1 minute. Add tomatoes, crushing with your hands as you add them. Cook, stirring frequently, until liquid is evaporated and tomatoes begin to stick to the bottom of the pot, 10-15 minutes.

Add broth, beans, thyme, marjoram, bay leaf, and reserved greens; season with salt and pepper. Bring to a boil, reduce heat, and simmer until flavors meld and soup thickens slightly, 40-50 minutes. DO AHEAD: Soup can be made 2 days ahead. Let cool slightly; chill until cold. Cover and keep chilled. Reheat before continuing. Store bread airtight at room temperature.

Just before serving, gently stir bread and 1/4 cup oil into soup. Divide among bowls, top with Parmesan, and drizzle with oil.