Pat dry and season: Blot the pork with paper towels. Rub with salt and pepper on all sides.
Brown the pork (optional but recommended): Heat olive oil in a large skillet over medium-high.
Sear the pork 2–3 minutes per side until nicely browned. Transfer to the slow cooker.
Build the flavor base: Scatter sliced onion in the slow cooker. Add bay leaves if using.
Place the seared pork on top.
Make the sauce: In a bowl, whisk balsamic vinegar, chicken broth, Dijon, brown sugar or honey (if using), garlic, rosemary, and thyme. Pour over the pork.
Cook low and slow: Cover and cook on Low for 8–10 hours (ideal for pork shoulder) or High for 4–5 hours. The pork should be tender enough to shred with forks.
Shred and skim: Transfer pork to a cutting board and shred.
Skim excess fat from the cooking liquid.
Thicken the sauce (optional): Whisk cornstarch with 2 tablespoons cold water. Stir into the slow cooker juices. Cover and cook on High 10–15 minutes until slightly thickened, or simmer in a saucepan to reduce.
Finish and serve: Return shredded pork to the sauce and toss to coat.
Taste and adjust salt and pepper. Garnish with chopped parsley and serve warm.