Combine soy sauce, 4 Tbsp. water, 1 Tbsp. corn starch, and honey in a small bowl; mix well. Set aside.
Combine remaining 1 Tbsp. cornstarch and 2 Tbsp. water in a large bowl; mix well. Add beef. Toss gently to coat.
Heat oil in large skillet over medium-high heat.
Add beef; cook, stirring frequently, for 2 minutes, or until cooked through and no longer pink. Remove from skillet, keep warm.
Add broccoli, bell pepper, garlic, and ginger to skillet; cook, stirring frequently, for 3 to 5 minutes. Place broccoli mixture in beef bowl.
Add soy sauce mixture to skillet; cook, stirring constantly, over medium-high heat for 30 seconds, or until thickened.
Return beef and broccoli mixture to skillet; cook, for 1 to 2 minutes, or until well mixed and heated through.