Place a steamer basket in a large saucepan, and fill with 1 inch water; set aside for broccoli. Cook rice according to package instructions.
Meanwhile, make sauce: In a small bowl, combine honey, sesame seeds, soy sauce, and garlic; set aside. In a large bowl, whisk together egg whites and cornstarch. Add chicken; season with salt and pepper, and toss to coat.
In a large nonstick skillet, heat 1 tablespoon oil over medium-high. Add half the chicken; cook, turning occasionally, until golden and opaque throughout, 6 to 8 minutes. Transfer to a plate; repeat with remaining tablespoon oil and chicken. Return all the chicken to skillet; add reserved sauce and scallions, and toss to coat.
Meanwhile, place saucepan with steamer basket over high heat; bring water to a boil. Add broccoli, and cook until crisp-tender, 4 to 6 minutes. Serve sesame chicken with broccoli and rice.