Begin by carefully cutting the beef short ribs into manageable pieces, ensuring they are uniform for even cooking. Next, peel and cube the potatoes and carrots, creating bite-sized chunks that will soak up the flavorful sauce. Chop the onion finely and mince the garlic and ginger.

In the slow cooker, layer the beef short ribs at the bottom, followed by the potatoes and carrots. Add in the chopped onion, minced garlic, and ginger. Pour the soy sauce, beef broth, honey, and sesame oil over the top, ensuring everything is well-distributed.

Cover the slow cooker with its lid and set it to cook on low for about 6 hours. Check for doneness; the short ribs should be tender and easily falling off the bone.

Once cooked, ladle the tender rib mixture over a bed of white rice. Spoon some of the savory-sweet sauce over top. Finish with toasted sesame seeds and chopped green onions.