Preheat oven to 375. Heat 1 tablespoon olive oil in a 12-inch cast iron skillet on medium heat.
Add garlic and saute for 30 seconds, then add breadcrumbs and stir until lightly browned and toasted. Remove breadcrumbs and garlic to a plate and set aside.
Add 2 tablespoons olive oil to skillet and when heated, add onion. Cook onion on medium-low heat for 5-10 minutes until translucent and starting to caramelize.
Gently toss remaining vegetables with the last 2 tablespoons olive oil, salt, pepper, and fresh herbs, and starting at one edge of the skillet begin layering the vegetables in concentric circles, working from the outside in and overlapping each piece.
Try to compact the vegetables so they all fit, but you'll probably have some leftover. Drizzle a little olive oil over the vegetables then top with the parmesan cheese and the breadcrumbs. Bake for 35-40 minutes, until vegetables are tender.
Notes
Make-ahead - to make the vegetable gratin ahead, leave off the cheese and breadcrumbs and just roast the vegetables. Refrigerate until almost ready to serve. Bring to room temperature, then add the cheese and breadcrumbs and toast in the oven.
Storage - store the leftovers in an airtight container in the refrigerator for up to 2 days.