Rinse, stem, and seed bell pepper; trim out and discard white veins. Cut pepper into strips about 1/4 inch wide and 2 inches long.
Rinse beef and pat dry. Cut across the grain into 1/16- to 1/8-inch-thick slices, then cut slices into bite-size pieces.
Pour oil into a 10- to 12-inch nonstick frying pan over high heat. When oil is hot, add bell pepper and stir just until tender-crisp to bite, about 3 minutes. Pour from pan into a bowl.
Add beef to pan and stir just until no longer pink, about 2 minutes. With a slotted spoon, transfer meat to bowl with pepper.
To meat juices in pan, add lime juice, honey, hoisin sauce, soy sauce, ginger, and chili flakes. Boil over high heat, stirring often, until mixture is reduced to about 1/3 cup, 5 to 6 minutes. Pour beef and bell pepper back into pan and stir until hot, about 30 seconds.
Spoon beef stir-fry onto plates and sprinkle with cilantro.