Preheat oven to 400 degrees.
Mix chili powder, paprika, thyme, salt, pepper, and brown sugar.
Pat pork roast dry with paper towels and place in a roasting pan or dutch oven. Rub all sides of the roast with chili powder mixture. Scatter quartered onions, garlic cloves, quartered apple and bay leaves around the edges.
Whisk together one cup of pomegranate juice and tomato paste and pour around roast. Add beer and then enough water for the liquids to surround half of the roast.
Cover the pan with the lid or aluminum foil and braise in oven for 30 minutes.
Remove from oven and flip the roast over in the braising liquid.
Reduce heat to 300 degrees and return to oven.
Allow roast to braise for 2-3 hours. Larger roasts may take longer.
Check the roast each hour to ensure liquid has not completely evaporated. Add a cup of water/beer/juice as needed.
Roast is done when it can easily be pulled apart with two forks.
Carefully remove roast to another dish (like a 9x13 pan).
If using a bone-in roast, the bone should release cleanly and easily from the meat when fully cooked. Discard bone, bay leaves and any large apple pieces.
Shred pork with forks, removing any excess fat.
Allow braising liquid to cool and skim excess fat off the top. Ladle liquid, a cup at a time, over shredded meat just until lightly coated. Reserve extra liquid for leftovers or heat in a saucepan to reduce to a thicker sauce.