Preheat the oven to 375 degrees. Coat a baking sheet with olive oil cooking spray.
Combine the olive oil, red wine vinegar, balsamic vinegar, maple syrup, basil and oregano together in a large bowl. Season with sea salt and freshly cracked pepper, to taste; whisk until well combined.
Toss the carrot pieces in the well whisked vinaigrette until coated evenly. Place the carrots on the prepared baking sheet.
Toss the beet wedges and garlic cloves in the vinaigrette then place them on the baking sheet. Set the remaining vinaigrette aside for later use.
Roast for 15 minutes then flip the veggies over. Continue to roast for another 15 minutes. Cover with foil and continue to roast for another 15-20 minutes, or until fork tender.
Remove the baking sheet from the oven and drizzle the remaining vinaigrette all over the veggies on the baking sheet; toss to coat evenly.
Place the carrots, beets and garlic cloves on a serving plate then top with feta cheese. Serve immediately. Enjoy.