2 tablespoons extra-virgin olive oil 1/4 cup finely diced pancetta 2 cups large diced Savoy cabbage 1 cup medium diced yellow onion 1 cup sliced carrot (1/4 inch thick) 1/4 cup medium diced celery 2 cloves garlic, minced 2 quarts defatted low-sodium chicken broth 1 can (14 1/2 ounce size) diced tomatoes with their juices 1/2 cup pearl barley, rinsed 2 large sprigs fresh rosemary Parmigiano Reggiano rind (optional) kosher salt 1 cup canned kidney beans -- (rinsed and drained) freshly ground black pepper Freshly grated Parmigiano Reggiano -- for serving
Heat the oil in a heavy 6-quart or larger pot over medium heat. Add the pancetta and cook, stirring frequently, until it becomes ever so slightly golden, 2 to 3 minutes.
Add the cabbage, onion, carrot, celery, and garlic. Cook, stirring frequently, until the vegetables begin to soften, about 6 minutes.
Add the broth, the tomatoes with their juices, the barley, rosemary, Parmigiano rind (if using), 1/2 teaspoon salt, and 1 cup water. Bring to a boil over high heat, and then reduce the heat to a simmer and cook until the barley and vegetables are tender, about 20 minutes.
Discard the rosemary sprigs and Parmigiano rind. Stir in the beans and season, to taste with salt and pepper. Serve sprinkled with the grated Parmigiano.