Place the chicken in the bottom of a 6-quart or larger slow cooker. In a medium mixing bowl or large measuring cup, whisk together the soy sauce, honey, tomato paste, chili paste, garlic, and rice vinegar. Pour the mixture over the chicken. Cover and cook on LOW for 4 to 5 hours or HIGH for 2 to 3 hours, until the chicken reaches an internal temperature of 165°F when tested with an instant-read thermometer. If possible, flip the chicken once halfway through cooking to ensure both sides are coated (though it's not necessary if you can't).

Once the chicken is done, remove it to a plate and let it cool slightly. Whisk the cornstarch into the cooking liquid in the slow cooker. Cover and cook on HIGH for 15 minutes, or until the sauce thickens slightly, stirring occasionally. If you prefer a thicker sauce, you can cook it for an additional 30 minutes in the slow cooker or follow the stovetop method below.

For quicker sauce thickening, transfer the cooking liquid to a medium saucepan after whisking in the cornstarch. Cook over medium heat, stirring frequently, for 5 to 10 minutes until the sauce thickens. (If your slow cooker insert is stovetop-safe, you can place it directly on the burner, but only do this if you're certain your insert is stovetop-safe to avoid cracking.)

Once the chicken has cooled enough to handle, shred it using two forks or your fingers. Add the shredded chicken back into the slow cooker, and if you reduced the sauce on the stovetop, pour it back into the slow cooker as well. Stir to coat the chicken with the sauce. Serve over rice, and top with chopped green onions and sesame seeds.