Preheat oven to 400 degrees F. In a large bowl stir together oil, lemon peel, salt, and pepper. Add beets; toss to coat. Divide beet mixture among six jumbo (3 1/2-inch) muffin cups or six 6-oz. custard cups set in a shallow baking pan. Cover cups with foil. Bake for 25 to 35 minutes or until beets are just tender when pierced with a fork.
Meanwhile, on a lightly floured surface, roll out pastry to a 12x10-inch rectangle. Using a 4-inch round cutter, cut pastry into 6 circles. (Keep pastry circles chilled until ready to use.)
Remove pan from oven. Uncover beets and top each cup with a pastry cutout. Carefully tuck pastry into edge of cups to cover beets. Return to oven and bake for 15 to 20 minutes more or until pastry is puffed and golden. Cool on a wire rack for 5 minutes. Meanwhile, stir together goat cheese and snipped fresh thyme. Loosen pastry from sides of cups. Place a serving plate over muffin cups and invert tarts onto plate, replacing any beet wedges that may fall off. Top each tart with goat cheese mixture and fresh thyme leaves and additional lemon peel, if desired.