Heat oil in a Dutch oven over medium-high heat until just smoking.
Sear the roast until well browned on all sides, about 3 minutes per side.
Turn the roast fat side up.
Scatter the onion and garlic around the roast and cook until fragrant and beginning to brown, about 2 minutes.
Add 1 3/4 cups of cider, the thyme sprigs, bay leaves, and cinnamon stick and bring to a simmer.
Cover, transfer to the oven, and braise until a fork slips easily in and out of the meat and the meat registers 190 degrees, 2 1/4 to 2 3/4 hours.