Preheat the oven to 360F, with the baking sheet inside
Core apples, cut into quarters and loosely chop (1” -2” thin pieces)
Combine the apple pieces, 1/4 cup sugar, rum, lime juice, chopped pecans, vanilla extract, and raisins or currants in a small bowl
Melt the butter in a small pan over low heat. Add the graham cracker crumbs, cinnamon and 1 Tbsp sugar. Stir for 1 minute
Add half of the graham cracker crumbs, mixture to the apple slices
Sprinkle flour on your work surface (I use a silpat mat). Unfold the puff pastry sheet and roll the pastry sheet int a 16 x 12-inch rectangle. With the long side facing you, spread the rest of the graham cracker crumb mixture even onto the middle this of the puff pastry sheet, leaving 2 inches all around the edge.
Spoon the apple mixture in the middle 4 - 5 inches all down the length. Fold the lower half of pastry over the apple mixture picking up the silpat from the bottom. Repeat with the top 1/2 crossing over about 1 - 2 inches. Tuck the ends under to seal.
Pick up with silpat and transfer to hot pan, with the strudel seam on the bottom.
Make 5 -6 slits with a serrated knife across the top and brush with the egg. Bake for 35 - 40 minutes until the apple strudel is golden brown.
