In a medium bowl, combine the brown sugar, balsamic vinegar, soy sauce, chicken broth, minced garlic, dried thyme, salt, and black pepper. Whisk together until the brown sugar is fully dissolved.
Place the pork shoulder in the crockpot and pour the prepared sauce over it, ensuring the meat is well-coated.
Cover the crockpot with the lid and cook on low for about 6 hours, or until the pork is tender and can easily be shredded with a fork.
Once cooked, carefully remove the pork from the crockpot using tongs and set it on a cutting board. Shred the meat using two forks.
If you prefer a thicker sauce, mix the cornstarch and water together in a small bowl to create a slurry. Stir this mixture into the sauce in the crockpot and cook for an additional 15-30 minutes on high until thickened.
Return the shredded pork to the crockpot, stir to combine with the thickened sauce, and let it warm through for about 10 minutes.
Serve the brown sugar balsamic glazed pork over rice, mashed potatoes, or alongside roasted vegetables.