Spread a sheet of phyllo dough on the countertop and brush half of it with butter. Fold sheet in two, bringing the non-buttered side over the buttered half. Brush half with butter, and fold again. Repeat once more, then cut the resulting rectangle in two. Brush top with butter, and place on a baking sheet covered with parchment paper. Repeat this process with the three other sheets of phyllo dough.
Preheat oven to 350°F (180°C) and bake phyllo squares 8 to 10 minutes or until they are lightly golden and well done. Oven crisps may be prepared the day before and kept at room temperature in an airtight metal container (do not use plastic as this will soften the crisps).
Mix nuts and maple syrup, and place mixture on a baking sheet covered with parchment paper. Roast in oven at 350°F (180°C) for 8 to 10 minutes or until nuts are roasted and slightly caramelized. Remove from oven and let cool.
Place cheese slices on four crisps, sprinkle mixed nuts on top, and add apple slices. Cover with another crisp, then bake in oven about 5 minutes or until cheese starts to run. Garnish with mixed nuts and serve immediately.
