Trim both ends of beets; wrap in foil and place on rimmed baking sheet. Place carrots on same baking sheet; toss with oil. Roast in 400°F (200°C) oven for 25 to 30 minutes or until carrots are tender. Remove carrots and set aside. Continue roasting beets for 15 to 30 minutes or until tender when pierced with sharp knife. Unwrap and let beets cool slightly; slip off skins. Cut into 1/2-inch (1 cm) rounds.

Meanwhile, in small saucepan, stir together sugar and water. Cook over medium-high heat, swirling pan occasionally, until mixture is amber-coloured, 4 to 6 minutes. Remove from heat; add vinegar. Quickly pour caramel into 9-inch (23 cm) glass pie plate; tilt and rotate pan to evenly coat bottom with caramel. 

Arrange beets and carrots in single layer on top of caramel. Sprinkle with cheese and rosemary.

Place pie crust over vegetables, tucking edges into pan. Prick dough all over with fork. Bake in 400°F (200°C) oven for 20 minutes; reduce heat to 350°F (180°C) and bake until crust is golden brown, 15 minutes. Let cool 10 minutes before inverting carefully onto large rimmed plate. Sprinkle with parsley.