Using mandoline or vegetable peeler, shave carrots into long, thin ribbons. Gently run ribbons through sauce, making sure they are evenly coated and place in single layers on baking sheet. Brush strips with remaining sauce and set aside for 5 minutes for flavors to fully absorb into ribbons. Bake in center of preheated oven for 10 to 15 minutes, turning strips halfway through cooking for even browning. Remove sheet from oven and set aside. Ribbons will still be slightly soft but will harden as they cool. Sprinkle with additional salt, if you wish.