Preheat oven to 325°F (165°C).
Pat pork shoulder dry and season with salt and black pepper.
Heat olive oil in a Dutch oven over medium-high heat.
Sear pork on all sides until deeply browned.
Remove pork and set aside.
Add sliced onions to the pot and sauté until softened.
Add garlic and cook until fragrant.
Pour in apple cider and scrape up browned bits from the bottom.
Stir in chicken broth and apple cider vinegar.
Return pork to the pot and add thyme and bay leaves.
Cover with lid and transfer to the oven.
Braise for 2½ to 3 hours until pork is fork-tender.
Remove from oven and let rest before slicing or shredding.