In 8 inch (20 cm) oven proof skillet, heat oil over medium high heat; saute 1/2 mushrooms, red pepper, onions and salt, stirring often, until softened, about 3 minutes. Sprinkle with bean sprouts. Pour in eggs; reduce heat to medium and cook, without stirring, until almost set, about 5 minutes. Place skillet under broiler; broil until golden, about 1 minute. Run small spatula around side of pan and slide egg onto cutting board. Cut into quarters; cut each into 1/2 inch (1 cm) wide slices. Set aside.
Dressing: meanwhile, in small bowl, whisk together vegetable oil, rice vinegar, sesame oil, soy sauce, honey, ginger and garlic; set aside. Place greens and cucumber in bowl; drizzle with 1/3 cup (75 mL) of the dressing and toss. Arrange on plates. Sprinkle with sesame seeds. Arrange egg slices over top; drizzle with remaining dressing.
Preparation: 10 minutes
Cooking: 8 minutes