Toast dried guajillo and ancho chilies in a large dry skillet over medium heat for 1-2 minutes per side until fragrant and slightly darkened but not blackened. Remove stems and seeds, then soak chilies in 2 cups hot water for 15 minutes until softened.
6 pieces dried guajillo chilies, 3 pieces dried ancho chilies
Blend softened chilies and 1 cup of soaking liquid in a blender. Add garlic, half the chopped onion, cumin, and oregano. Blend on high for 1-2 minutes until completely smooth. Strain through a fine-mesh sieve to remove any gritty bits.
6 pieces dried guajillo chilies, 3 pieces dried ancho chilies, 1 medium onion, 6 cloves garlic, 1 tbsp cumin, 2 tsp oregano
Bring chicken broth to a boil in a large stockpot. Add chicken thighs, remaining quartered onion, and strained chili sauce. Reduce heat and maintain a gentle simmer at 180-200°F. Cover and cook for 45-60 minutes, skimming fat every 20 minutes. Use a meat thermometer to check chicken is done at 165°F.
2 lbs chicken thighs, 1 medium onion, 8 cups chicken broth
Remove chicken from broth and let cool for 5 minutes. Add drained hominy to the broth and simmer uncovered for 20-30 minutes. Shred the chicken with two forks and return it to the pot. Taste and adjust seasoning with salt as needed.
2 lbs chicken thighs, 2 cans hominy
Ladle the pozole into bowls and top with shredded cabbage, sliced radishes, chopped cilantro, and a squeeze of lime. Serve with warm corn tortillas on the side if desired.
shredded cabbage, sliced radishes, fresh cilantro, lime wedges