Peel and cut potatoes into 1 inch cubes. Cut carrot, green peppers, and onion into large chunks.
In a small bowl, combine soy sauce, sugar, rice wine, garlic, honey, pepper, and water.
In a small pot, sauté the potatoes and carrots in vegetable oil over medium heat for 4 - 5 minutes.
Add sauce mix to pot and bring it to a boil over high heat. Cover, and reduce the heat to medium and cook until the potatoes are tender (about 7 or 8 minutes - less if cut potatoes are smaller).
Stir in green peppers and onion and continue to boil uncovered for an additional 3-4 minutes until sauce is reduced to a thick sauce, just enough to cover bottom of the pan.
Stir in sesame oil and sesame seeds before serving.