In a dry skillet over medium heat, toast the guajillo and ancho chiles for 1-2 minutes per side until fragrant. Place them in a bowl, cover with hot water, and soak for 15 minutes until softened. Drain.
In a blender, combine the soaked chiles, onion, garlic, oregano, cumin, and 1 cup of the chicken broth. Blend until very smooth. Strain through a fine-mesh sieve into a bowl for an extra silky broth (optional).
Heat oil in a large pot or Dutch oven over medium-high. Season chicken thighs with salt and sear for 3 minutes per side until golden. Add the chile puree and remaining 3 cups broth. Bring to a boil, then reduce heat, cover, and simmer for 15 minutes.
Add the drained hominy to the pot and continue simmering uncovered for 15-20 minutes, until the chicken reaches an internal temperature of 165°F (74°C) and the flavors meld. Remove the chicken, shred with two forks, and return to the pot. Season with salt to taste.
Ladle the pozole into bowls and let everyone add their own toppings: shredded cabbage, radishes, cilantro, and a squeeze of lime. Serve with tortilla chips or tostadas on the side.