Place the pork shoulder in a large bowl for marinating (make sure it will fit in the fridge).
Pour the lime juice over the pork.
Prepare the marinade by mixing the garlic, ground cumin, salt and pepper in a mini-food processor. You can also crush the garlic with a press and mix with the cumin, salt & pepper. If you want the extra rich red color, you can also add a tablespoon of achiote or annato powder to the mix.
Make several deep incisions on both sides of pork shoulder and begin stuffing the incisions with the garlic cumin marinade, also rub it all over the meat. Mix the remaining garlic cumin mix with the beer, and pour it over the pork shoulder and let it rest overnight the fridge. If you have time you can let it rest 24 hours, if not overnight is fine.
Turn the pork shoulder over every 8-12 hours.
Pre-heat oven to 400F (200C) and place the pork shoulder or pork loin (with the marinade sauce) in a baking pan, with the skin side up, make sure it is deep enough to allow room for the marinade and also a little extra room to add the potatoes later on.
In a small saucepan, melt a stick of butter on low heat, stir in 1 tablespoon of the ground achiote and mix well.
Drizzle and brush the melted achiote butter mix all over the dry pork skin. Keep any remaining butter mix to use to baste the pork skin during baking.
Bake the pork at 400F for about ~30 minutes.
Lower the oven temperature to 350F and bake for 1 ½ hours. To keep the pork from drying out you will need to baste or bathe the meat using a ladle with the pan sauces about every 20-30 minutes. You can use the achiote butter to baste the skin.
Lower the oven temperature to 325F.
The pan sauces might be reduced at this point, so melt the remaining ½ butter stick on low heat, mix in 2 cups of beer plus the remaining 1 tablespoon of ground achiote, and let it get hot but not boil. Use the mix as needed to keep the pork moist.
Continue baking and bathing for another 1 ½ hour. At this point you can add the whole or cut in half potatoes. Let the potatoes and pork bake for about another hour.
Total roasting time should be around 4 ½ hours for an 8-10 pound pork shoulder, or about 25-30 minutes per pound, internal temperature should be 160.
Before removing the pork from the oven, sprinkle cold water on the skin for it to pop –this might not work with a smaller piece of pork. If this doesn’t work, then you can turn the broiler on for a few minutes to help the skin get crispy. Or alternatively, after carving the meat, remove the skin, and scrape off the fat from underneath. Then cut the skin into medium size pieces and put them under the broiler for about 3-5 minutes or until they get crispy and start to pop (when they pop they squirt oil so just a warning).
Serve the pork with mote or hominy (plain or sautéed with the hornado gravy), the potatoes that were baked with the pork or llapingachos potato patties, tomato and onion curtido salsa, agrio sauce, avocado slices and aji criollo.