Whisk together balsamic vinegar, water, and next 5 ingredients.
Add pork to slow cooker. Pour the balsamic vinegar mixture over the pork. Cover and cook on low for 8 hours or high for 4-5 hours.
Use a small strainer or a spoon to discard fat from the liquid in the slow cooker. Transfer as much liquid from the slow cooker into a medium saucepan. Bring liquid to boil. Whisk together and cold water and corn starch and stir into the boiling sauce. Reduce to simmer and allow to cook for 3-4 minutes until slightly thickened. Shred pork with 2 forks, pour sauce over the meat and serve.