Preheat oven to 375 degrees. Spray a baking sheet with nonfat cooking spray. Place diced carrots and beets onto baking sheets, and lightly mist with an olive oil mister or nonfat cooking spray. Season with salt and pepper. Roast in oven until tender, about 40 minutes.
In a small bowl, whisk together the oil, honey, lemon juice, salt and pepper.
Add arugula and basil to a large bowl, and toss well with the dressing.
Top with the roasted carrots, beets and feta cheese and serve right away.