Mix all the bulgogi sauce ingredients in a small bowl and set aside. Put beef in a bowl and mix the shiitake mushrooms and marinade and give it a good mix.

Heat oil in a skillet over medium high heat. Add onion and white part of green onions and cook until soft, about 1-2 minutes. Add ground beef and cook until beef is browned and fully cooked.

Allow the mixture to simmer until it is heated through and the sauce reduces, about 2 minutes. If using mix in the peppers and cook for one minute. Serve immediately over steamed rice and garnish with green onion and sesame seeds, if desired