Trim bottom from boy choy heads. Cut leaves from stalks. Cut stalks into 1/2-inch chunks. Gather large leaves and cut into halves.
Heat vegetable oil over high heat. Saute bok choy stalks and bell pepper in hot oil until just beginning to soften, about 1 minute.
Stir garlic, ginger, and red pepper flakes into the bok choy mixture; saute until garlic and ginger are fragrant, about 1 minute more.
Stir bok choy leaves, soy sauce, and sesame oil into the bok choy mixture; saute just until the leaves turn a bright green and beginning to soften, about 1 minute more.
