Combine teriyaki sauce, water, honey, cider vinegar, ground ginger, orange zest, and pepper in a small bowl.

Transfer 3/4 cup of the marinade to a large bowl.

Add minced garlic and sesame oil to the large bowl.

Score the surface of the flank steak in a diamond pattern, about 1/4 inch deep.

Place the steak in the bowl with the marinade, turning to coat.

Cover the bowl and refrigerate for at least 8 hours, or overnight.

Cover and refrigerate the remaining marinade for basting.

Drain and discard the marinade from the steak.

Lightly oil the grill rack.

Grill the steak over medium heat, covered, or broil 4 inches from the heat for 7-10 minutes per side.

Cook to desired doneness (135°F for medium-rare, 140°F for medium, 145°F for medium-well), basting occasionally with 3 tablespoons of the reserved marinade.

Let the steak stand for 5 minutes before slicing across the grain.

Heat the remaining marinade.

Serve the sliced beef with the heated marinade.

Sprinkle with chopped green onion.