Melt the butter in a small, heavy-bottomed saucepan over low heat. Do not stir. Skim off the milk solids that float to the surface and set the remaining butter aside.
Unwrap the fillo dough and cut it into two manageable sections.
Some brands come in smaller portions already, while others, like this Kontos brand, come in 14″ X 18″ sheets. After cutting them in half, you should end up with two 14″ X 9″ sections.
(Roll up half of the fillo sheets for another time, making sure they are sealed in the plastic and store in the freezer.)
Preheat oven to 350-degrees F.
Cover fillo sheets with plastic, or parchment paper, followed by a damp washcloth to keep the sheets from drying out.
Place another large sheet of parchment paper next to the sheets of fillo dough. This will be used to assemble the apple strudel.
Place a sheet of fillo on the parchment paper and brush with butter. Sprinkle with 1 tablespoon finely ground walnuts.
Dust with powdered sugar. Continue these steps until you have used up 1/2 of the sheets (approximately 8 to 10 sheets).
Generously brush the last sheet of fillo dough with butter.
Pile half of the apple mixture on the fillo dough close to one edge, leaving a 2″ border from the top, bottom, and one of the sides.
Lift up on the parchment paper to fold the top, bottom, and side with the 2″ border over the apple filling. Generously baste with the reserved apple juices.
Continue rolling the dough over the filling until you have a tight package.
Brush the top with additional apple juices and butter.
Using a spatula, place the strudel on a pan lined with parchment paper. Bake for 25 to 30 minutes or until brown and crispy.
While the first strudel is cooking, assemble the second strudel using the remaining ingredients.
Cool for at least 15 minutes before slicing. Sprinkle the baked strudel with powdered sugar before serving.