Soak skewers. If you are using wooden skewers, submerge them in water for at least 30 minutes before using.
Prep onion. Peel and half the onion, then cut into quarters. Cut each quarter into 1-inch thick slices.
Prep peppers. Seed and core the peppers and cut into slices the same size as the onion.
Prep squash and eggplant. Remove the ends of the zucchini, squash, and eggplant, and slice into 1/2-inch thick slices.
Prep mushrooms. Wipe mushrooms clean with a paper towel and cut in half if large.
Marinate and skewer. Toss all vegetables in a large bowl. Toss with garlic, olive oil, salt, and pepper. Then skewer onto the soaked wooden or metal skewers. Depending on the size of your skewers you should have 10-12 skewers total.
Heat grill. Heat gas or charcoal grill to medium heat.
Prepare the vinaigrette. Combine all ingredients except the olive oil in a medium bowl. Stir to combine. Slowly stir in olive oil until well combined.
Grill. Grill skewers over medium heat, turning occasionally, until tender and lightly charred, about 15-20 minutes.
Serve. Transfer to a serving platter and spoon vinaigrette over the skewers. Serve with extra vinaigrette on the side.