If desired, heat olive oil in a skillet over medium-high heat. Sear the pork shoulder on all sides until browned, about 3-4 minutes per side.
In a mixing bowl, whisk together the brown sugar, balsamic vinegar, soy sauce, dijon mustard, minced garlic, black pepper, and salt until well combined.
Place the pork shoulder in the Crockpot. Pour the balsamic glaze mixture over the pork, ensuring it is well-coated.
Cover the Crockpot and cook on low for 6 hours, or until the pork is tender and easily shredded with a fork.
Once cooked, remove the pork from the Crockpot and let it rest for a few minutes.
Optionally thicken the sauce by cooking it on high for 15-20 minutes with the lid off.
Shred the pork using two forks and then return it to the sauce, mixing well to coat.
Serve hot, garnished with fresh parsley if desired.