Preheat oven to 350 degrees and line a baking sheet with parchment paper.
Spread the diced veggies (including the whole pieces of garlic) out on the baking sheet and drizzle with olive oil, salt, pepper and oregano. Place in the oven and bake for 20-25 minutes, or until the veggies are tender.
While the veggies are cooking, bring a large pot of water to a boil. Add the pasta and cook according to the package instructions. Drain and rinse under cold water.
Prepare the dressing by combining all of the ingredients in a bowl and whisking until combined. Cover and place in the fridge until ready to use.
Once the veggies are cool, remove the garlic from the baking sheet and roughly chop them. Add all of the veggies (including the garlic) to a large bowl with the drained pasta. Place in the fridge for at least an hour.
When you are ready to serve, add the dressing to the pasta/veggies and toss to combine. Top with green onion, peperoncini peppers and vegan parmesan.