Combine first 3 ingredients in a bowl, stirring well; sprinkle evenly over steak. Combine cornstarch, sugar, and red pepper in a medium bowl, stirring well with a whisk. Stir in broth and soy sauce.
Heat oil in a large nonstick skillet over medium-high heat. Add carrot to pan; stir-fry 2 minutes. Add steak and broccoli; stir-fry 1 minute. Stir in broth mixture; cook 1 minute, stirring constantly. Add snow peas; cook 30 seconds or until desired degree of doneness. Serve with rice.