Make the sponge and the bun dough: combine all ingredients for the sponge in a medium mixing bowl and let set, until mixture starts to rise. In a separate bowl add water, milk, and egg and mix well. In a mixer, add 3 1/4 cup of flour, 1/3 cup sugar, and 3 tablespoons of shortening; add the egg, milk, and water mixture. Mix with a dough hook until combined. Then add the sponge mixture and mix. The dough must rest 12 to 24 hours before use. When ready to use, roll out dough into bun sizes. Steam in a steamer for 5 to 6 minutes.
Make the pulled pork: combine all ingredients in a pot and cook over low to medium low heart for two hours or until the meat falls apart and the sauce is thick. Remove pork shoulder from pot, shred the meat with two forks, return the meat to the pot and combine with the sauce.
Make the glaze: add oil to a pan over high heat. Add the sofrito and mustard sauté until the sofrito vegetable are soft. Add the rest of the ingredients and cook, stirring occasionally, until sauce thickens enough to coat back of spoon, about 2 minutes more.
Make the relish: add all the ingredients to a pan over medium heat and cook slowly for about 30 minutes until the relish reaches a syrup consistency.
To build buns: top one bun with 1 tablespoon of shredded pork. Top with 1 teaspoon of glaze and 1 tablespoon of relish. Serve immediately.