Cut tortillas in half. Place tortillas on a baking sheet and lightly coat with nonstick cooking spray.
Sprinkle 1/4 teaspoon pumpkin pie spice over tortilla halves. Bake for about 10 minutes or until crisp. Cool completely on a wire rack.
Peel, core, and slice apples.
Lightly coat a medium, nonstick skillet with cooking spray and preheat over medium heat. Add apples, brown sugar and remaining 1/2 teaspoon pumpkin pie spice; cook and stir about 10 minutes or until golden.
Add currants. Continue cooking, stirring occasionally, about 20 minutes or until the apples caramelize and the liquid evaporates.
Place each tortilla half on a dessert plate and spoon apple mixture over tortillas.