Wash broccoli; cut broccoli off stalk into florets; set aside.
Finely mince onion; set aside.
Combine melted butter, lemon juice, onion and seasonings in a small bowl or glass measuring cup.
Place broccoli on top of wire rack on heated grill over medium heat.
With a pastry brush, brush the broccoli with butter sauce.
Cook broccoli for three minutes, basting at least once per minute while grilling.
Turn broccoli over and grill remaining side.
Brush butter sauce over remaining side at least once per minute.
Grill broccoli about 6-10 minutes (about 3 minutes per side) or until tender.
The time will depend on the heat of the grill.
Remove from grill to serving platter.
If you have any remaining butter mixture, baste broccoli again.
Serve.