In a large nonstick skillet, heat the olive oil until very hot. Add the carrots, red onion and celery. Cook over medium heat until the vegetables begin to slightly caramelize and soften in texture, about 10 minutes. Add the apples, currants, apple juice, vinegar, honey and dijon mustard. Cover, reduce heat to a simmer, and cook 10 minutes more. Remove the cover, and boil until the liquid has evaporated and the vegetables begin to glaze. Stir in the chopped basil and season to taste with salt and pepper. Serve at once.