Slice pork belly into 1½-inch-thick strips, then cut strips crosswise into 1½-inch-thick pieces. Transfer pork to large bowl, sprinkle with salt and pepper, and toss until evenly coated. Cover and refrigerate for at least 12 hours or up to 24 hours.

Pat pork dry with paper towels. Heat oil in large Dutch oven over medium-high heat until just smoking. Add half of pork and cook, turning occasionally, until fat is rendered and pork is well browned on all sides, 12 to 15 minutes. Using slotted spoon, transfer pork to large plate. Repeat with remaining pork. Pour off fat from pot and reserve for another use.

Add wine and sugar to now-empty pot and stir until sugar is dissolved, about 30 seconds. Add thyme sprigs and pork and bring to simmer over medium-high heat. Cover; reduce heat to low; and simmer until pork is tender, 1½ to 2 hours, stirring once halfway through cooking.

Using slotted spoon, transfer pork to large plate; discard thyme sprigs. Cook wine mixture over high heat, stirring often, until sauce is thick and syrupy and registers 225 degrees, 10 to 15 minutes. Off heat, return pork to sauce and stir to coat. Let cool for 10 minutes, then stir again to coat with sauce. Serve.