Pozole served at posada gatherings warms guests during the Christmas celebration season. This high protein, family tradition dish is a fresh, hearty, festive soup for holiday nights.
Cube the pork shoulder into large pieces. In a large pot over medium-high heat, add pork, 1 chopped onion, half of the garlic cloves, bay leaves, and cover with water (about 12 cups). Bring to a simmer, skimming off any foam.
Reduce the heat to low and gently simmer the pork uncovered for 1.5–2 hours until tender, occasionally removing excess fat from the surface.
While pork simmers, toast dried guajillo chiles in a dry skillet over medium heat for 2 minutes, pressing with a spatula, until fragrant but not burnt. Remove stems and seeds, then soak chiles in 1 cup hot water for 15 minutes.
Blend soaked chiles with the remaining garlic cloves, 1/2 cup of the simmering pork broth, and oregano until smooth. Strain if desired. Add chile mixture and hominy to the pot, stirring carefully to combine. Season with salt and black pepper.
Simmer everything together uncovered over low heat for 30–45 more minutes, adjusting salt to taste. Before serving, slice radishes, shred green cabbage, and cut limes for garnish. Ladle pozole into bowls and serve topped with radish, cabbage, and lime wedges.