1) If you are using wooden skewers, soak them in plenty of water for about 10 minutes if griddling on an indoor griddle pan or for 30 minutes if griddling on an outdoor griddle to prevent them from burning.
2)Place all of the veggies in a large bowl or baking dish. Drizzle with olive oil and season with salt, pepper and garlic. With your hands, toss to combine well. Stick the onion pieces in with the vegetables to coat with the marinade; avoid tossing once the onion is added so that the onion does not fall apart.
3) Alternate the vegetables with the onions on wooden or metal skewers. The onions will get nice and juicy rubbing up against the other veggies. You can do this up to a few hours before you griddle them.
4) Preheat a griddle pan over medium-high heat.
5) Arrange the skewers on the griddle pan and cook, turning often, until slightly charred, about 15 minutes. Remove from the griddle and serve hot or at room temperature.
*Cook's note: To get skewer-able chunks of onion, cut the onions in half through the core and then cut each half into quarters. Remove two or three of the innermost layers, leaving the larger outermost layers. They will fit nicely on your skewers.