Soak the currants in hot water to cover for 30 minutes. Drain and reserve 1/4 cup soaking liquid.
Thinly slice the carrots or cut into julienne on a mandoline. You should have about 5 cups.
Heat the butter in a large saute pan over low heat. Add the sugar, spices, and carrots. Cook, stirring constantly, 2-3 minutes. Stir in the orange juice and currants with reserved soaking liquid. Turn up heat to bring to boiling, then reduce heat and simmer, covered, until tender. Season to taste with salt and pepper. Sprinkle with mint or parsley and serve hot.