Preheat the oven to 400°F. Line a baking sheet with parchment paper.
To make the filling, mix the cubed apples, granulated sugar, brown sugar, cinnamon, lemon juice, and chopped walnuts together in a bowl.
Place one sheet of the phyllo dough on the parchment-lined baking sheet and brush it with melted butter. Repeat with the remaining sheets, brushing butter between each layer.
Spoon the apple/walnut filling along one long edge of the stacked phyllo, leaving 2 inches at the sides.
Carefully roll the phyllo over the filling, tucking in the sides as you go. Make sure the strudel is seam-side down.
Brush the top of the strudel with the remaining melted butter. Sprinkle with coarse sugar if desired.
Bake the strudel for 30–35 minutes, or until it is golden brown and crisp.
Allow the strudel to rest for 10–15 minutes before slicing. Serve it warm with powdered sugar and/or vanilla ice cream. Enjoy!