The night before serving, sort through the beans and discard any small, cracked or shriveled ones. Place the beans in a pot or jar large enough to cover them with water by at least 3 inches. Leave the beans in a cool place or in the refrigerator overnight to rehydrate.
The next day, strain the beans through a colander (discard the water). Add the beans to a medium saucepan with enough water to cover by at least 2 inches, about from the tip of your finger to your knuckle. Turn the heat to medium-high, bring the liquid to a boil, then return to a simmer and cook, stirring occasionally and skimming off any foam that rises to the top, until the beans are tender, 50 minutes to 1 hour. Add additional water when necessary to keep the beans submerged. When the beans are done, turn off the heat, add 1 1/2 teaspoons salt and stir to incorporate; set aside.
Put the salt pork in a medium pot over medium heat and cook, stirring occasionally, until crispy, about 12 minutes. Remove the salt pork and discard. Pour off all but 2 tablespoons of the fat. Add the tomato paste to the pot, and cook until it darkens, about 2 minutes. Add 2 cups of the cooking water from the beans, and simmer for 10 minutes. Strain the beans, add them to the pot and cook just long enough to heat them through, about 5 minutes.
Meanwhile, bring a large pot of generously salted water to a rolling boil, and cook the pasta according to the package directions for al dente. Add as many pasta shapes as you wish, as long as their cooking times are within 2 minutes of one another (according to the package directions). Drain, reserving 2 cups of the cooking water. Add the pasta back to the pot, add the beans with their liquid and the reserved pasta water and stir in 2 to 3 teaspoons of pepper. Ladle the soup into serving bowls, and grate the Pecorino Romano over the top if using.
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