Whisk together soy sauce, vinegar, honey, sesame oil, garlic, ginger, salt, and pepper in a medium bowl.
Divide marinade between two bowls. Add beef cubes to one bowl and mix well, marinating for 30 minutes at room temperature or up to 8 hours in the fridge.
Separate broccoli into 16 similar-sized florets. Trim stems and halve large florets if necessary.
If using wooden skewers, soak them in water for at least 20 minutes to prevent burning.
Thread skewers with alternating pieces of scallion, broccoli, and beef. Repeat until you have 8 skewers.
Generously brush skewers with reserved marinade and lightly season with additional salt and pepper.
To grill: Preheat grill to high and cook skewers for 3-4 minutes per side for medium-rare. Brush with extra marinade as needed.
To broil: Set broiler to high and place skewers on a foil-lined baking sheet. Broil for 4 minutes per side, brushing with marinade for added flavor.
Serve immediately.