Prepare the Pork Shoulder:
Preheat your oven to 325°F (163°C). Pat the pork shoulder dry with paper towels and rub with salt, black pepper, and dried thyme.
Sear the Pork:
Heat olive oil in a large oven-safe skillet or Dutch oven over medium-high heat. Sear the pork on all sides until browned, about 2-3 minutes per side.
Create the Base:
Add minced garlic to the pan and sauté until fragrant, about 30 seconds. Pour in chicken stock to deglaze the pan, scraping any browned bits from the bottom.
Braise the Pork:
Add black cherries and balsamic vinegar to the pan. Cover with a lid or foil and transfer to the oven. Cook for 2.5 hours, basting occasionally.
Make the Reduction:
Remove the pork from the pan and set aside to rest. Strain the cooking liquid into a small saucepan. Add honey and simmer over medium heat until the sauce thickens to a syrupy consistency.
Serve:
Slice the pork shoulder and drizzle with the black cherry reduction. Serve warm with your choice of sides.