1. When the vegetables are cool enough to handle, thread four mushrooms onto four of the skewers, about one inch (two and a half centimeters) apart, leaving a small space at the top. Repeat with four cherry tomatoes on four additional skewers and a combination of peppers and onions on the remaining four skewers.
2. Starting at the pointed end of the skewer, weave a dough strip down and around the vegetables, pinching at the bottom to secure, and place on a baking sheet lined with Gefen Parchment-. Repeat with the remaining skewers, placing six skewers on each sheet.
3. Brush the skewers with olive oil and season with additional salt, pepper, garlic powder, and Italian seasoning. Sprinkle lightly with Parmesan cheese. Bake for 12–15 minutes until lightly browned, switching the pans between upper and lower racks midway through baking. Serve immediately.