Heat a large, dry frying pan over medium-high heat. Add chiles, garlic, and 1/2 of 1 yellow onion, quartered. Watch vegetables closely, turning as they toast. Remove the chiles to a plate as soon as they are toasted and fragrant so they don't burn. Garlic will also be done before the onion, then finally the onion, which will take about 10 minutes to char on all sides.

Bring a medium saucepan of water to a boil. Add toasted chiles and submerge under the water. Remove pan from the heat and let chiles soak until tender, about 15-20 minutes.

Remove chiles from the water and add to a blender, along with charred onions and garlic, oregano, cumin, apple cider vinegar, and a teaspoon or so of salt. Blend with 1/4 cup or so of the Chile-soaking water until smooth (you may need to add a bit more liquid to get the blender going). Taste and add more salt if needed.

Heat oven to 300°F. Season lamb on all sides generously with salt and pepper. Chop remaining onions.

Heat a large oven-safe dutch oven with a lid over medium-high heat. Add lamb and brown on all sides, about 10 minutes. Remove to a plate.

Add remaining onions, carrots, and celery, and season with salt. Cook, stirring occasionally, until browned, about 10 minutes. Add chicken broth and scrape up any browned bits from the bottom of the pot. Stir in guajillo sauce. Add lamb and return to a boil.

Cover and place in the oven. Braise until lamb is very tender, and easily comes apart with a fork, about 3-4 hours.

Shred lamb and toss with the sauce. Combine baby arugula and red onion in a large bowl. Squeeze the half lime over the vegetables and drizzle with the oil. Season with salt, toss to combine.

Place a generous amount of braised lamb on each tostada shell, top with salad and serve.