Preheat oven to 325 degrees F.
Season the pork with salt and pepper. Combine 2 tablespoon olive oil with 2 teaspoon cumin, 1 teaspoon oregano, 1 teaspoon paprika, and 1 teaspoon coriander. Rub the spice mix on the pork. Place the cut onion and 4 cloves garlic in the bottom of a baking dish and pour 2 cups chicken broth in the pan. Place the pork on top, wrap with foil and roast in the oven for 2 - 2 ½ hours or until fork tender. The pork should easily shred with a fork when ready. Shred and keep warm until ready to make sandwiches.
While the pork is roasting, prepare the pickled red onions. Heat the vinegar in the microwave for 30 seconds and add the sugar and salt. Stir until dissolved and pour over the red onions. Let sit for at least 5 minutes or overnight.
Prepare the aji cilantro sauce. Blend together 1 aji pepper with ½ bunch cilantro, 5 green onions, 2 garlic cloves, the juice of ½ lime, and ¼ cup olive oil. Season with salt and pepper.
Mash the avocados and season with salt and lime juice. Spread a generous portion of the avocado on each of the buns, about ½ an avocado per sandwich. Top with the shredded pork, pickled onions and aji sauce. Serve immediately.