Prep the pork. Trim any thick, waxy pieces of fat from the pork shoulder. Cut into 2–3 large chunks to help it cook evenly and absorb more flavor.
Season well. Mix salt, pepper, smoked paprika, and dried thyme.
Rub the blend all over the pork, pressing it into the surface.
Sear for extra flavor (optional but recommended). Heat olive oil in a large skillet over medium-high. Sear pork on all sides until browned, about 2–3 minutes per side. Transfer to the slow cooker.
Layer the aromatics. Scatter the sliced onion in the bottom of the slow cooker.
Add the minced garlic on top.
Make the cooking sauce. In a bowl, whisk together brown sugar, balsamic vinegar, chicken broth, tomato paste, Dijon, and red pepper flakes (if using). Pour over the pork.
Cook low and slow. Cover and cook on LOW for 8–10 hours or HIGH for 4–5 hours, until the pork is fork-tender and shreds easily.
Shred the pork. Transfer the pork to a large bowl. Skim excess fat from the surface of the cooking liquid.
Shred the meat with two forks, discarding any fatty bits.
Thicken the sauce (optional). Turn the slow cooker to HIGH. Mix cornstarch with water to make a slurry and whisk it into the cooking liquid. Cover and cook 10–15 minutes until slightly thickened and glossy.
Glaze and serve. Return shredded pork to the slow cooker.
Toss to coat in the sauce. Taste and adjust seasoning with a pinch of salt, pepper, or a splash more balsamic if you want extra tang. Serve warm.