Trim the vegetables and cut them, with the exception of the mushrooms and scallions, 1/4 inch thick. Discard the mushroom stems, and leave the scallions whole.
Combine all the marinade ingredients in a large bowl or sealable plastic bag. Mix and crush the ingredients with your hands, directly or through the bag, squeezing them to release the maximum flavor.
Toss the vegetables in the marinade and let them absorb the flavors for no longer than 30 minutes.
Direct Grilling - Preheat the BBQ to medium-high. Drain the vegetables, reserving the marinade, and put them on the well-oiled grill.
Pour the marinade into a foil pan or heatproof pan and set on the grill.