Cutting the vegetables roughly the same size will ensure that they cook at a similar rate. About 1 inch dice works well here. Feel free to change up the vegetables here as well as the spices to alter the flavor profile.
Preheat the oven to 400ºF and line a rimmed baking sheet with parchment paper. Set aside.
Toss the vegetables with olive oil, salt, garlic, and thyme then spread onto the prepared baking sheet. Roast in the oven until the vegetables begin to brown, about 35 minutes. Then stir and continue roasting until brown again, another 10-15 minutes. Remove from oven, transfer to a serving dish and drizzle with balsamic, stirring to distribute. Taste and adjust seasoning with salt and pepper. Serve with Parmesan, if desired.