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Step 1
In a medium bowl, whisk together the soy sauce, vinegar, honey, sesame oil, garlic, ginger and 1/2 teaspoon kosher salt. Season with black pepper.
Step 2
Divide the marinade between 2 medium bowls. Add the meat to 1 bowl and toss to coat. Leave to marinate for 30 minutes at room temperature, stirring occasionally, or cover and refrigerate for up to 8 hours.
Step 3
Separate the broccoli into 16 florets (you may have some extra broccoli). They should each be 1 to 1 1/2 inches, cut any particularly big florets in half and trim the stems.
Step 4
Meanwhile, if using wooden skewers, soak them in water for at least 20 minutes so they don't burn on the grill. Drain before threading the skewers.
Step 5
When the meat is ready, make the skewers: Thread 1 piece scallion perpendicular to the skewer, then carefully thread 1 broccoli floret onto the skewer, then 1 piece of beef. Repeat with another layer of scallion, broccoli, beef, then finish with the last of the scallion. Repeat with all the ingredients to make 8 skewers.
Step 6
Brush the skewers generously with the reserved marinade then season with a pinch of salt and black pepper.
Step 7
To grill: Prepare the grill on high heat. Grill the skewers to desired doneness, about 3 to 4 minutes per side for medium-rare, brushing with the remaining marinade. Serve right away.
Step 8
To broil: Heat the broiler to high and position the rack about six inches away. Line a baking sheet with foil and add the skewers. Broil until the meat is cooked to desired doneness, about 4 minutes per side for medium-rare, brushing with the remaining marinade.