Ingredients
Method
Season 1 lb. pork shoulder (Boston butt), cut into 1" pieces, all over with kosher salt and freshly ground pepper. Heat 2 Tbsp. extra-virgin olive oil in a medium Dutch oven over medium-high. Cook meat in a single layer, turning halfway through, until deeply browned, about 4 minutes.
Add 4 garlic cloves, finely chopped, and 4½ tsp. chicken bouillon paste to pot and cook, stirring often to avoid burning garlic, until meat is coated, about 1 minute. Sprinkle in 2 Tbsp. all-purpose flour and cook, stirring, until no dry streaks remain, about 1 minute.
Add 1 white onion, halved, peeled, 2 bay leaves, 1½ tsp. oregano, preferably Mexican, and 6 cups water. Increase heat to high; bring to a boil. Reduce heat so soup is at a simmer, cover, and cook until pork is tender and soup has thickened slightly, 45–55 minutes.
Add two 15-oz. cans white hominy, rinsed, and cook, uncovered, until tender (meat will be even more tender at this point), 20–30 minutes. Taste soup and season with salt.
Ladle soup among bowls; top with thinly sliced green cabbage, thinly sliced radishes, cilantro leaves with tender stems, and sliced avocado. Serve with tostadas and lime wedges for squeezing over. Do Ahead: Soup (without toppings) can be made 5 days ahead. Let cool; cover and chill. Reheat over medium before serving.