Peel and cut beets into wedges. Peel and cut carrots into 1 1/2" pieces, then cut in half. Set aside.
In a large bowl, whisk olive oil, balsamic vinegar, red wine vinegar, maple syrup and salt until well combined. Add the oregano, pepper and basil and whisk some more. Add the chopped vegetables and mix well to ensure even coverage.
Transfer the vegetables, including garlic, to a baking tray lined with parchment paper or aluminum foil.
Roast at 375F for 30 minutes, then cover with aluminum foil can continue baking for another 30 minutes or until the vegetables have reached the desired tenderness.
Transfer the roasted vegetables to a platter, drizzle with some olive oil, sprinkle with crumbled feta cheese, garnish with fresh cilantro and serve.