1Preheat the oven to 375°F. Season the lamb shanks with salt and pepper.
2Heat 1 tablespoon olive oil in an enameled cast-iron Dutch oven (or heavy-bottomed pot with lid) over medium-high heat. Add 2 shanks at a time, turning regularly, until browned on all sides. Repeat with one tablespoon of olive oil and remaining shanks and set aside.
3Add half each of the onion, celery, carrot, and all of the garlic. Sautee, stirring occasionally, until golden, about 5 minutes. Stir in the dried cilantro, oregano, bay leaf, half of the cumin, the intact half of the jalapeño, and half of the guajillo chiles. Top the mixture with the shanks and any juices and add the chicken stock and beer. Cover tightly and braise in the oven for about 2 hours or until the lamb is very tender.
4In a heatproof bowl, combine remaining guajillo chiles and 1 cup of boiling water. Soak, covered, for 30 minutes. Transfer the chiles and half of the liquid to a blender and puree until smooth.
5Remove lamb from the pot to a baking sheet and tent with foil. Strain the broth into a separate container, discarding any solids. Skim any fat and wipe out the pot with a paper towel.
6Heat remaining one tablespoon of olive oil in the pot. Add the remaining onion, celery, carrot, and diced jalapeño and sauté over medium heat, stirring occasionally, until golden, about 5 minutes. Stir in the chili puree, coriander, remaining cumin, and hominy and cook for 2 minutes. Add the reserved broth and simmer for 10 minutes. Stir in the lime juice and season to taste with salt and pepper.
7Add the shanks (left whole or meat pulled off of the bone) and cook until just heated through, about 5 minutes. Serve in bowls and garnish with fresh cilantro, lime wedges, Cotija cheese, and avocado.