This is my Hungarian grandmother's recipe for strudel, but I suspect they were so poor when she was little they couldn't afford to buy apples to make the traditional filling. If you saute cabbage in butter and sweeten it a bit, it tastes and feels a lot like cooked apples. So I think that's why she did that. I remember her making it when I was little, but she never taught me. Later, as I was rummaging through her recipe card files, I found the secret recipe! Of course she made her strudel dough from scratch. In those days families were big with lots of children, so there were plenty of hands to stand all around the table and pull strudel dough. Nowadays, with 2.5 children and two working parents, there's no way to do it at home. I have my grandmother's white linen tablecloths from her dowry, which were always put down to cover the gigantic dining room table to pull the dough on. I think these good linen tablecloths were primarily used for pulling strudel dough versus having company over for a lavish meal, which would have been pricey then and possibly beyond my family's means.
Make the Filling: Heat the butter in a large skillet over medium-high heat. Add the cabbage and cook, stirring, until tender. Add the sugar and salt and stir to dissolve. Add the raisins and cook, stirring, to reduce the juices and let them soak into the raisins, about 3 to 4 minutes. Stir in the walnuts and spread on a baking sheet to cool.
Make the Strudel: Preheat the oven to 375 degrees F.
Arrange a parchment-lined baking sheet on the counter, so it's horizontal to your body. Place 1 sheet of phyllo on the pan. Using a pastry brush, spatter the phyllo with some of the melted butter; then brush to cover with the butter. Sprinkle with 1/3 of the sugar and 1/3 of the chopped walnuts. Repeat with the 2 remaining sheets of phyllo. Reserve the remaining melted butter and sugar.
Spoon the cooled cabbage filling 2 inches in from the bottom edge of the phyllo, working from left to right, leaving 2 inches bare at the left and right. Roll up the pastry, lifting the parchment paper, to encase the filling, forming a log. Move the log to the center of the sheet pan and tuck the ends under to keep the filling from oozing out. Brush the surface with melted butter and sprinkle with sugar. Bake until golden brown, about 30 minutes. Let cool 10 to 15 minutes on the pan. Using a serrated knife, cut carefully into sections and serve warm.