Place the roast in a slow cooker and top it with the sliced bell peppers and snap peas. In a bowl, whisk together the soy sauce, honey, sesame oil, ginger, garlic, vinegar, sesame seeds, and beef broth. Pour the mixture over the vegetables. Set the crock pot to high for 5 hours or low for 7-8 hours.
Remove the beef from the crock pot and place it on a cutting board. Scoop out about 1/4 cup of the liquid from the pot and whisk it together with the cornstarch. Stir the mixture back into the pot along with the mushrooms. Cover and cook for an additional 20-30 minutes on high, or until the sauce is slightly thickened. Meanwhile, shred the beef and prepare some rice to go with it, if you'd like.
Add the beef back into the slow cooker and stir to cover it in the sauce.
To serve, ladle the beef over rice and top with additional sliced peppers, chives, and sesame seeds.