Preheat oven to 350°.
Leave root and 1-inch stem on beets; scrub with a brush. Place beets, 2 tablespoons olive oil, 1 tablespoon garlic, 1 teaspoon thyme, and 1 teaspoon tarragon in a large bowl; toss gently. Place beet mixture on a jelly-roll pan. Bake at 350° for 1 hour or until beets are tender. Drain and cool slightly. Trim off beet roots; rub off skins. Cut in half. Sprinkle with 1/2 teaspoon salt and 1/2 teaspoon pepper.
Combine vinegar, sugar, shallots, 2 tablespoons oil, 1 tablespoon garlic, 1/2 teaspoon thyme, 1/2 teaspoon tarragon, 1/2 teaspoon salt, 1/2 teaspoon pepper, and oregano in a small bowl, stirring with a whisk. Add vinegar mixture and onion to beet mixture; toss gently.