Trim any excess fat or sinew off the ribs. In a heavy skillet over medium-high heat, brown half of the ribs well on all sides, about 8 minutes total, then remove the ribs to a 4-quart slow cooker (they will fit better in an oval cooker); repeat with the remaining ribs. Pour ½ cup water into the skillet and scrape up all the browned bits in the bottom of the pan. Pour the liquid over the ribs in the cooker.

In a medium bowl, combine half of the scallions and all the remaining ingredients except the sesame seeds, stirring until the brown sugar is dissolved. Pour the mixture over the ribs. Cook, covered, on the low setting for 4 hours, or until the meat is very tender and almost falling off the bones.

In a small skillet over medium-high heat, toast the sesame seeds, shaking the skillet and stirring constantly, until they just begin to color. Transfer to a small bowl and set aside.

Remove the ribs from the sauce and place on a large serving platter or on individual plates. Spoon a little of the sauce over the ribs and sprinkle with the sesame seeds and the remaining scallions. Serve.