For a complete meal, serve this salad with pita bread, feta cheese, and hummus. If you are on a low-sodium diet, substitute a less-salty cheese for the feta.
Preheat oven to 375 degrees. Toss beets with 1 teaspoon oil on a rimmed baking sheet. Cover sheet with foil. Roast beets until tender, 45 to 55 minutes. Let cool. Trim and peel beets; cut into 1/2-inch cubes.
Meanwhile, toss carrots, 1 teaspoon oil, and 1/4 teaspoon salt on another rimmed baking sheet. Roast carrots until browned and tender, about 40 minutes. Let cool to room temperature.
Stir lemon juice, remaining 1/4 teaspoon salt, the parsley, and thyme in a small bowl. Whisk in remaining 2 tablespoons oil until emulsified. Season with pepper. Toss beets and carrots with dressing in a medium bowl. To serve, divide salad, pita, feta, and hummus among 4 plates. Drizzle oil over feta and hummus on each plate.
Salad can be refrigerated in an airtight container up to 3 days.