Preparation

Prepare the hominy

• Rinse and drain the hominy. Place it in a deep container and cover with enough cold water to completely submerge the hominy. Soak the hominy, covered, in the refrigerator for 2 days.
• To cook the hominy, rinse and drain the soaked hominy and combine it in a stockpot with cold water to cover by 8 to 10 inches. Bring to a boil, then decrease the heat to low and simmer, partly covered, until the hominy is tender and opens up into blossoms, about 3 hours. Ladle out 1 quart (4 cups) of the cooking liquid, strain it through a fine-mesh sieve, and set aside. Drain the hominy of all remaining liquid.

Make the clam broth

• Combine the quahogs, onion, celery, garlic, white wine, and white peppercorns in a stockpot and bring to a boil. Cook until the clams just begin to open and the wine is reduced by half.
• Add the cold water and bring to a simmer. Cook over low heat until all the clams are open, about 20 minutes. Discard any that don’t open. Lift the clams out of the broth and set them aside. Strain the broth through a fine-mesh sieve lined with a double layer of cheesecloth. Remove the clams from their shells and discard the shells. Chop the clams into bite-size pieces and set aside.

Make the soup

• Combine the clam broth, reserved hominy cooking liquid, and cooked hominy in a stockpot and bring to a boil over medium heat. Lower the heat and simmer for 30 minutes.
• Meanwhile, combine the onions, garlic, tomatillos, poblano and serrano chiles, and dried oregano in a blender and purée the mixture until it is very smooth. Add the cilantro and continue puréeing until the cilantro is completely incorporated and the mixture is vibrant green. Slowly add the oil in a thin stream until the purée is emulsified. Season to taste with salt.
• Add the purée to the hominy and cook 5 minutes. Add the chopped quahog clams and littlenecks to the soup and cook just until the littlenecks open, 2 to 3 minutes. Discard any that don’t open. Stir in the crabmeat and the cabbage and heat the soup just to warm through. Season to taste with salt.
• To serve, divide the soup among eight warmed soup bowls and garnish with the avocados, radishes, oregano, onion, and cilantro.