Step 1

Heat 3 tablespoons of the oil in a 6- to 8-quart Dutch oven or wide, heavy pot over medium heat.

Step 2

Add the celery, carrots, onion, garlic and 1/4 teaspoon salt. Cook, stirring occasionally, until the vegetables begin to soften, about 5 minutes.

Step 3

Stir in the tomato paste, then add the canned tomatoes with their juices, the Parmesan rind, pepper flakes and 5 cups water. Bring to a gentle simmer, breaking up the tomatoes with a wooden spoon, and cook until the vegetables are very tender, 20 to 25 minutes.

Step 4

Add the kale and simmer until just tender, about 10 minutes.

Step 5

Add the tender greens, including the chard stems, if using, and the beans. Continue cooking until the greens are tender, 8 to 10 minutes more. Remove and discard the Parmesan rind.

Step 6

Remove the soup from the heat, stir in the toasted bread pieces, and let stand for 5 minutes. Add the remaining 1/4 cup olive oil and stir well to break up the bread so that it blends into the soup a bit. Adjust the seasoning to taste. Serve hot, with pepper flakes and grated or shaved Parmesan on top.