Rub the pork with 1 Tablespoon salt and pepper, a teaspoon of paprika, and one of the smashed garlic cloves. Place in a plastic zip bag or plastic storage container. Store in the fridge overnight or a for a few hours before cooking.
Preheat oven to 300 degrees. Using a sharp knife, score fat (but not meat) on pork in a diamond pattern. Pulse herbs and the rest of the garlic in a food processor until combined. Slowly add oil and continue pulsing until a thick paste forms. Stir in 1 Tablespoons salt, 1 Tablespoon pepper; rub mixture all over pork.
Place the onion slices in a foil lined roasting pan or large Dutch oven. Place pork, fat-side up, on top of the onion halves; add 1 1/2 cups water to bottom of the pan. Drizzle a little bit of olive oil (about 1 Tablespoon) on top of the pork. Cover with foil or lid (if in a Dutch oven) and roast until meat is starting to become tender, about 3 hours. Remove foil or lid and continue cooking until meat is fork-tender, 1 to 1 1/2 hours more. Cook 30 minutes per pound total, or until the internal temperature as measured with a meat thermoter is 160 F. Remove pork from the oven and allow to rest 15 minutes before pulling apart or cutting.
Carefully transfer pork to a large bowl, leaving juices in pan. When cool enough to handle, use two forks to shred meat into bite-size pieces, discarding any large pieces of fat. Transfer shredded pork back to pot and toss with juices. If you prefer to serve in larger pieces as we did, transfer to a cutting board and slice your pork into desired thickness.