Add the olive oil to a large 2-gallon pot and heat over medium heat. Add onions, garlic, and carrots, gently season with salt, and sauté for 10 to 12 minutes or until browned.

Next, add the whole chicken, celery, bay leaf, and 1 gallon of water. Simmer over low to medium heat for 75 to 80 minutes or until the chicken is thoroughly cooked through.

Carefully remove the chicken from the pot and set it to the side on a plate. Strain the stock into a separate large pot and put the strained vegetables, minus the bay leaf, to the side.

Add the hominy to the pot with the strained stock and heat over low to medium heat.

While the chicken is cooking, add the seeded chiles to a large cast-iron or carbon steel pan and cook them over medium heat for 2 to 3 minutes, pressing down on each chile for a few seconds at a time using a spoon or spatula.

Cover them entirely in water and simmer over low heat for 30 minutes or until softened.

In addition, optionally toast the cumin seeds in a medium-sized skillet over low to medium heat while constantly stirring until very fragrant, about 4 to 5 minutes.

Transfer the seeds to a mortar and pestle or spice grinder and grind until finely ground.

Once the chicken is done cooking and strained, add the veggies to a blender with 2 cups of strained stock, softened chiles (not the liquid), cumin, oregano, vinegar, cilantro, and salt, and blend until smooth. Add it to the pot with the stock and hominy.

At this point, the chicken should be cool to the touch. Remove the skin, pull the meat away from the bones, and shred it with your hands. Add it to the pot and cook for 20 to 25 minutes to marry the flavors.

Finish with salt and an optional hint of half lemon or lime juice. Serve with optional toppings.