Heat a large skillet over medium-high heat. In a small bowl, stir together the paprika, salt and pepper, then rub that evenly all over the pork roast. Spray the pan with nonstick spray, then add the roast to the pan; cook 10 minutes, turning to brown on all sides. Place the pork in your slow cooker.
Add the chicken broth, balsamic vinegar, molasses, soy sauce and red pepper to the skillet; bring this mixture to a boil, scraping the pan to loosen any browned bits. Whisk in the preserves. Pour the mixture over the pork in the slow cooker, then top with the onion and the garlic. Cover and cook on LOW 6½ hours, or until the pork is pull-away tender. Remove the pork from the slow cooker (keep the liquid!), shred it apart using two forks and transfer to a bowl. Use a slotted spoon to remove the onion, and add that to the pork. Cover with foil. Pour the hot liquid from the slow cooker into a medium saucepan. Stir in the bourbon and bring to a boil. Cook 15 to 20 minutes, or until the mixture is reduced to about 1½ cups. Combine 2 tablespoons cold water and the cornstarch in a small bowl, stirring until smooth. Whisk this mixture into the sauce, stirring constantly over low heat until it has thickened slightly. Stir in remaining ¾ teaspoon salt. Pour the sauce over the pork and toss to coat.
MAKE THE COLE SLAW:
In a medium-large bowl, whisk together the mayo, sugar, vinegar and salt. Add the coleslaw and the onion, and toss well to combine.
FOR SERVING:
Pile a generous serving of pulled pork onto the bottom half of a slider bun. Top with the coleslaw, then top with the other half of the bun. Repeat, serve and eat!
Notes
*If you are serving this as GLUTEN-FREE, omit the buns from the recipe (or use GF buns), and just be sure to use brands of mayo, peach preserves, soy sauce, molasses and chicken broth that are known to be GF.