Step 1Place the pork in a large stew pot with a lid and cover with water. Add 1 tablespoon salt and bring to a boil over high heat. Reduce the heat to a very low simmer, cover and cook until the pork is cooked through, about 2 hours, occasionally skimming any foam from the top with a large spoon. (It is OK if the pork is still medium rare/pink in the center.) Remove the pork from the broth and set aside until cool enough to handle, saving the broth.
Step 2While the pork is cooling, remove the stems and seeds from the chiles by opening each chile with your fingers or a small knife and scraping out the seeds. In a grill pan over medium-high heat, toast the chile pods in batches, pressing down with a spatula occasionally, until they begin to darken in spots and blister, about 1 minute per side. Place the toasted chiles in the pork broth until slightly softened, about 10 minutes, and remove to a bowl.
Step 3Place a small strainer on top of a large liquid measuring cup and strain 1 cup of the pork broth into the cup. Discard the remaining broth (or save it for another use) and wipe out the pot with a paper towel.
Step 4When the pork is cool, trim the thick layer of fat from the top and discard. Chop the pork into roughly one-half-inch cubes and place the meat in the stew pot, discarding the bone. Sprinkle the meat with 1 tablespoon salt.
Step 5In a blender, combine the garlic, half the softened chile peppers and chicken broth. Blend on medium-high speed until pureed and pour over the pork. Repeat with the remaining chile peppers, any juices that have accumulated in the chile pepper bowl and reserved 1 cup of pork broth. Stir well to combine.
Step 6Bring the pork to a gentle simmer and cook, covered, until the meat is tender, 2 to 3 hours. Stir every 10 minutes or so to make sure the mixture does not burn on the bottom of the pan. Remove from heat and season if desired with additional salt. This makes about 8 cups.
Step 7If the sauce is a bit thin, it can be thickened with cornstarch: In a small bowl, combine the cornstarch with 1 tablespoon water. Stir well and pour over the pork. Stir to combine, increase the heat and boil until the sauce is slightly thickened, about 2 to 3 minutes. Remove from the heat and season with additional salt to taste.
Step 8Arrange the bolillos, onions, avocado, chilantro and jalapenos on a serving platter. Allow guests to spoon the pork and sauce onto the bolillos and add the garnishes as desired.