Combine chicken and 1 tablespoon soy sauce, tossing to coat.
Heat canola oil in a Dutch oven over medium-high heat. Add shallots, ginger, and garlic; sauté 10 seconds. Add chicken mixture and mushrooms; sauté 4 minutes. Add rice, 2 tablespoons soy sauce, sesame oil, and red pepper; cook 1 minute, stirring constantly. Add bok choy; cook 2 minutes, stirring constantly.
Push rice mixture to one side of pan. Add egg to empty side of pan; cook 1 minute or until almost set, stirring constantly. Stir egg into rice mixture. Sprinkle with sesame seeds.