Wash and cut peppers, onions and broccoli spears. With a damp cloth, gently wipe debris from mushrooms.
Carefully spear vegetables onto bamboo skewers. I like to arrange the veggies in the order of pepper, onion, broccoli & mushroom. Note: If desired, you may soak the bamboo skewers in water before using, but I feel it is not necessary due to their being soaked well with the marinade.
Place skewers in a large, rectangular resealable container. Pour dressing liberally over veggies. Marinate for 6-12 hours or overnight, making sure to carefully flip the container upside-down and shake occasionally to redistribute the dressing.
Grill for 10-15 minutes over medium-high heat or until vegetables reach the desired crisp, done-ness.
To serve, slide vegetables off the skewer onto each person's plate.