Place the beef short ribs in the slow cooker.
In a bowl, stir together the soy sauce, brown sugar, garlic, ginger, sesame oil, and beef broth. Pour the mixture over the ribs.
Cover and cook on low for 8 hours until the meat is very tender.
About 30 minutes before serving, rinse the jasmine rice and cook it in a saucepan according to package directions.
In a separate bowl, combine the rice vinegar, sugar, and salt. Add the cucumber and carrots, then toss to coat. Let the vegetables sit for at least 15 minutes.
Remove the ribs from the slow cooker. Shred the meat from the bones if desired, or leave the pieces whole.
Divide the steamed rice among four bowls. Top with the short ribs and a spoonful of the pickled vegetables. Finish with sliced green onions and sesame seeds.