Prep the chiles: Remove stems and seeds from the guajillo and ancho chiles. Toast them in a dry skillet over medium heat for 30–45 seconds per side, just until fragrant.
Don’t burn them.
Soak the chiles: Place toasted chiles in a bowl and cover with hot water. Soak for 10–15 minutes until softened.
Blend the chile puree: In a blender, combine softened chiles with 1 cup chicken broth, 2 garlic cloves, and a small piece of onion (about 1/4 of an onion). Blend until very smooth.
Strain through a fine-mesh sieve for a silky broth, if you like.
Sauté aromatics: In a large pot, heat oil over medium. Add the remaining chopped onion and 2 minced garlic cloves. Cook 3–4 minutes until translucent and fragrant.
Bloom the spices: Stir in cumin and oregano.
Cook 30 seconds to wake up the flavors.
Add puree and simmer: Pour in the chile puree. Cook 2–3 minutes, stirring, until it slightly thickens and darkens. This step deepens the flavor.
Build the soup: Add chicken broth, bay leaf, hominy, and shredded chicken.
Bring to a gentle boil, then reduce to a simmer.
Season and balance: Simmer 15–20 minutes. Taste and season with salt and pepper. If desired, add a small pinch of bouillon for extra savoriness.
Finish with the juice of 1 lime for brightness.
Adjust texture: If you want it richer, simmer a bit longer to reduce. If it’s too thick, splash in more broth or water.
Serve with toppings: Ladle into bowls. Top with cabbage, radishes, cilantro, diced onion, avocado, and a squeeze of lime.
Add tortilla chips or tostadas for crunch.