Posole rojo simmers tender pork with hominy in a rich red chile broth for a traditional Mexican-American family celebration dish. This high protein, warming stew is garnished with fresh radish, cabbage, and lime.
Cut pork shoulder into 2-inch chunks, trimming excess fat, and season lightly with salt and pepper.
Place pork, onion, 3 garlic cloves, bay leaves, and 8 cups water in a large pot. Bring to a boil over high heat, then immediately reduce to a simmer. Skim foam and simmer gently for 1.5 hours, uncovered, until pork is tender.
Meanwhile, de-stem and de-seed guajillo and ancho chiles. Toast chiles in a dry skillet over medium heat for 1–2 minutes, turning to avoid burning, until fragrant.
Soak the toasted chiles in hot water for 15 minutes. Drain, then blend with 2 remaining garlic cloves and 1 cup pork cooking broth until smooth.
Stir chile puree, oregano, cumin, and drained hominy into the simmering pork. Continue cooking uncovered for 30–40 minutes, adjusting seasoning with salt as needed. Remove bay leaves before serving.
Ladle posole into bowls and garnish with shredded cabbage, radish slices, and fresh lime wedges.