Cook the Black Beans, If Needed: Cover dried black beans with water and soak them overnight, then drain and cook them in 6 cups of fresh water for about 1 hour, or until tender; season with salt to taste after cooking.
Sauté the Onion: Heat the vegetable oil in a Dutch oven or large soup pot over medium heat, add the finely chopped onion, and cook for 3–5 minutes, stirring occasionally, until the onion becomes translucent.
Add the Black Beans: Stir the cooked or canned black beans into the sautéed onion, then lightly mash some of the beans against the bottom or side of the pot with the back of a spoon to help give the broth a thicker consistency.
Add the Hominy: Pour in the vegetable broth or water, then add the cooked or canned hominy; stir everything together thoroughly.
Simmer the Pozole: Bring the mixture to a gentle simmer and cook for about 10 minutes, allowing the beans, hominy, onion, and broth to come together.
Adjust the Seasoning: Taste the pozole after simmering and add salt as needed.
Add the Toppings: Ladle the hot pozole into serving bowls, then garnish each bowl with diced avocado, dried Mexican oregano, sliced radishes, diced onion, and shredded lettuce or cabbage.
Serve: Serve the pozole warm, with corn tortillas or tortilla chips alongside if desired.
