Step 1

Place the onion, carrots, fennel, and garlic in the bowl of a food processor fitted with the blade attachment and pulse until very finely chopped but not pureéd. (Alternatively, chop the vegetables as finely as possible with a knife.)

Step 2

Heat the oil in a Dutch oven or large soup pot over medium heat until shimmering. Stir in the onion mixture and a big pinch of salt. Cook, stirring occasionally, until very soft, about 10 minutes. The vegetables will nearly melt into a sauce. Increase the heat to medium-high. Stir in the tomato paste and cook, stirring quickly and continuously, until the mixture begins to sizzle, about 1 minute.

Step 3

Stir in the broth and bring to a simmer. Stir in the cabbage and another big pinch of salt. Drop in the Parmesan rinds, if using. Simmer until the cabbage is very tender, stirring occaisonally, about 25 minutes. Retrieve the cheese rinds and either discard or nibble on them as a cook’s treat.

Step 4

Stir in the beans, thyme, and basil and simmer to warm through, about 5 minutes. Taste and season generously with salt, pepper, and pepper flakes as needed. Serve warm, drizzled with olive oil.