Preheat grill to medium heat.
Slice off the top third of each onion and set aside; save tops. Slice an "X" in the inner 2/3 off each onion. Using a spoon remove the inside of the onion forming a bowl. Dice the removed inner section of the onions and set aside.
In a medium bowl combine the vegetable medley, diced onion, herb garden seasoning and cheese. Evenly divide the mixture into each onion bowl. Top each filled onion with a tablespoon of butter.
Cover the onion with its original top. Wrap with 2 layers of foil and place on the grill or in a preheated 400 degree F oven. Grill or bake for 20 to 25 minutes or until onions are tender.