Preheat oven to 450° F. Line a large sheet tray with parchment and spread out vegetables. Drizzle with olive oil, season with salt and pepper, and sprinkle with thyme sprigs. Toss with your hands and spread into a single layer, making sure the vegetables have space between them to properly roast—if they are too close, roast in 2 batches to ensure they do not steam. Place on the center rack of the oven for 12 minutes, then toss. Return to the oven for an additional 8 to 10 minutes, or until the thickest part is fork tender.
Serve warm, garnished with more fresh thyme, as a side dish, chopped up on a winter salad, or as an appetizer with dips.