Mix the chopped yellow onion, chopped garlic, tomato paste, Dijon mustard, white vinegar, paprika, ketchup, Worcestershire sauce, Jack Daniels, brown sugar, black pepper, and bay leaf together.
Put the pork shoulder and sauce mixture in a large stock pot and cover with water. Bring to a boil and reduce to a simmer. Let the mixture simmer for two hours. You will know when it is done by the way the pork pulls apart so easily.
Take the pork out of the sauce a pull it apart. Then take the Jack Daniels sauce in the pan and reduce it to 1/3 of it's original amount. Mix the pork and the sauce together.