Melt the butter in a medium-size cast iron or nonstick pan over medium heat. Add the apples, sugar, and salt. Cook, stirring, until apples are tender and the sugar is melted and gooey,
Stir in cinnamon, cardamom, and breadcrumbs. Remove from heat and let cool.
Gently remove six fillo sheets from the package and cover them under a kitchen towel. They dry out pretty quickly, so it is important to keep them covered.
Place three sheets on a clean working surface. Cut the layered sheets into half lengthwise, then each half into thirds. You want to get six equal squares (trim the sheets if necessary).
Place a heaping tablespoon of the apple filling in the middle of a fillo square (it is best if you turn the square to look diamond-shaped). Fold up the bottom half and tightly fold in the sides. Gently roll, then seal the fold with a couple of drops of water. Repeat with the remaining apple mixture. (See GIF above in the post)
Heat the oil in a large skillet over medium heat (it should reach 1" up the side of the pan). Add the rolls and fry until golden, about one minute per side (do in batches). Transfer to a paper towel-lined plate to cool slightly.
Dust apple rolls with powdered sugar and serve with caramel sauce if desired.
Notes
Use thicker sheets of filo: It will ensure they don't burn or bust open during frying. If you must use thinner sheets (suitable for baklava), you might need to add a couple of sheets to the layers. If the sheets are smaller or shorter, cut them into four squares (you might need to make more squares to use up the filling). If you can't find thicker filo sheets at your local store (I find them at Whole Foods), you can get them on Amazon.
No need to brush the layers of fillo with oil or butter: we will fry them. If you wish to bake them instead, you'll need to butter each layer and then the rolls' tops. Bake at a high temperature until the rolls are golden brown and crispy, usually around 20-25 minutes at 375°F (190°C).
Keep filo dough covered: Filo dough dries out quickly, so keep it covered with a damp cloth while you work.
Cut evenly: Cut the filo sheets into even rectangles for uniform rolls before adding the filling.
Don't Overfill: Use no more than the suggested amount of apple filling to prevent it from seeping out and to ensure even cooking.
Seal the Edges: Roll tightly and tuck in the edges to keep the filling inside.
Cool Before Serving: Let the rolls cool slightly before serving to allow the filling to set and to avoid burns.
Please keep in mind that nutritional information is a rough estimate and can vary significantly based on the products used and serving size.
STORAGE:These filo pastry apple pie rolls are best enjoyed fresh, as the pastry will become soggy after some time.