Place a steamer basket in a large saucepan, and fill with 1 inch water; set aside for broccoli (only if using fresh 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, cook the broccoli. If using frozen florets, cook according to the package directions. If using fresh broccoli, 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.