Cut steak into 1 1/2″ cubes and place in a large storage bag or bowl.
In a small bowl, whisk together minced garlic, soy sauce, brown sugar, vinegar, and sesame oil. Reserve about a third of this sauce in the fridge for basting later.
Pour remaining marinade over steak cubes and toss to fully coat. Cover and place steak in the fridge to let marinade for at least 4 hours up to overnight.
Skewer the kabobs using 3 pieces of steak, 3 broccoli florets, and 3 slices of onion.
Grab the reserve marinade and whisk in ketchup and honey.
Heat your grill to medium heat.
Add skewers to the hot grill, turning every 2-3 minutes to cook all sides evenly for a total of about 15 minutes. During the last few turns, baste with sauce.
When done, skewers will have nice char marks and meat will be tender (about 145-150 degrees for a medium cook). If you like them more well done, leave on for a bit longer.
Serve skewers with a sprinkle of sesame seeds and chopped green onions. Enjoy with your favorite side dishes!