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Heat 2 Tbs. of the olive oil in a 4- to 5-qt. Dutch oven over medium heat. When hot, add the pancetta and cook, stirring frequently, until quite shrunken, golden brown, and crisp (the oil will also be golden brown), about 6 minutes. Remove the pan from the heat and with a slotted spoon or strainer carefully transfer the pancetta to a paper-towel-lined plate. Pour off and discard all but 2 Tbs. of the fat from the pan.
Return the pot to medium-high heat and add the chopped cabbage. Cook the cabbage, stirring occasionally, until limp and browned around the edges, about 3 minutes. Remove the pot from the heat again and transfer the cabbage to another plate.
Put the pot back over medium heat and add 2 Tbs. more of the olive oil. When the oil is hot, add the onions, carrots, and salt. Cook, stirring occasionally, until the onions are softened and the vegetables are browned around the edges and beginning to stick to the bottom of the pan, 8 to 9 minutes. Add the last 1 Tbs. of olive oil, the garlic, 1 Tbs. of the fresh rosemary, and the ground coriander and cook, stirring, until the garlic is fragrant, about 1 minute. Add the tomatoes, stir together, and cook the mixture 2 to 3 more minutes.
Return the cabbage to the pan and add the chicken broth. Stir well, bring to a boil, and reduce to a simmer. Cook for 10 to 15 minutes to infuse the broth with the flavor of the vegetables. Add the beans, bring back to a simmer, and cook for a minute or two. Remove the pan from the heat, stir in the remaining 1 tsp. fresh rosemary, and let rest a few minutes.
Taste the soup and add lemon juice to brighten it—you’ll want at least 1 tsp. Season with more salt if necessary and a few grinds of fresh pepper. Serve the soup hot, garnished with the reserved pancetta crisps, the toasted breadcrumbs, and the grated Parmigiano.
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