
Marinate the broccoli. Place broccoli and sliced onions into a large zip top bag. Combine the olive oil, vinegar, garlic, Italian seasoning, salt and pepper; drizzle over broccoli and toss to coat. Let stand for 30 minutes.
Preheat the grill. When ready to cook, start your grill and set the temperature to medium (around 300-350 degrees F.) Close the lid, and allow the grill to preheat for 10-15 minutes.
Grill the broccoli. Place the broccoli in a grilling basket to prevent the broccoli from sticking or falling through the grate. Roast the broccoli, turning once or twice for 8-10 minutes or until the pieces are bright green and tender crisp. There will likely be some slight char on a few pieces. This is good!
Serve the grilled broccoli. Remove the broccoli from the grill to a serving platter and serve.