Preheat the oven to 425 degrees. In a medium bowl, combine the apple, shallots, raisins, vinegar, brown sugar, ginger, and red pepper flakes. Let sit for 10 minutes.
To assemble: Heat the mountain bread, one at a time, directly over a gas flame or grill, or in a hot skillet, turning frequently, just until pliable, about 5 to 15 seconds each. Scatter 3 pieces of cheese in the center of a round of mountain bread. Top with a quarter of the apple chutney. Fold in the two sides and roll. Complete the wraps with the remaining ingredients. Or, if you prefer, prepare them all at once, assembly-line style.
To cook: Lightly oil a baking sheet and heat in the oven for 5 minutes. Carefully add the wraps, seam side down, and bake until crisp on one side, then turn and bake until the second side is crisp, about 10 minutes total. Remove from the oven and allow to sit for 5 minutes. Serve hot or warm, cut in half on the bias with a serrated knife.