Step 1

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

Step 2

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.

Step 3

Heat ¼ cup oil in a large heavy pot over medium heat. Add carrots, celery, and leek; stir often until softened, 8–10 minutes.

Step 4

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.

Step 5

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. Discard sprigs and bay leaf.

Step 6

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.

Step 7

Just before serving, gently stir bread and ¼ cup oil into soup. Divide among bowls, top with Parmesan, and drizzle with oil.