Heat 1 teaspoon sesame oil in a large nonstick skillet over medium heat. Pour in eggs; cook, stirring gently, until set, about 5 minutes. Transfer to a plate.
Heat remaining 2 teaspoons oil in the skillet. Add garlic and ginger; cook and stir until fragrant, about 2 minutes. Stir in bean sprouts, broccoli slaw, soy sauce, and rice vinegar; cook until broccoli slaw is tender, about 5 minutes.
Stir eggs and hoisin sauce into the skillet until eggs are in small pieces and heated through, about 3 minutes.