Prepare the Cabbage Filling: Heat butter or oil in a large pan over medium heat. Add the chopped onions and cook until they become soft and translucent, around 8-10 minutes. Add the shredded cabbage, caraway seeds, and paprika, stirring everything together. Season with salt and pepper. Continue to cook for 15-20 minutes, stirring occasionally, until the cabbage is tender and slightly caramelized. The filling should have a deep golden color for the best flavor.

Prepare the Dough: Preheat your oven to 375°F (190°C). If using phyllo dough, lay out a single sheet on a clean surface and brush it lightly with melted butter. Layer another sheet on top and repeat the process until you have five sheets stacked. This layering provides a flaky crust for your strudel.

Assemble the Strudel: Spoon the cabbage filling along one edge of the prepared dough, leaving space at the edges to fold in. Carefully roll the dough over the filling, tucking in the edges as you go. Place the rolled strudel seam-side down on a baking sheet lined with parchment paper. Brush the top with additional melted butter to help the strudel brown nicely.

Bake the Strudel: Bake the strudel for 30-40 minutes, or until the crust is golden and crisp. Keep an eye on it, especially if using phyllo dough, as it can brown quickly. Once baked, let it rest for a few minutes before slicing to make serving easier.

Serve and Enjoy: Slice the cabbage strudel into thick portions and serve with your preferred side dishes or sauces. This dish is best enjoyed warm, as the filling and crust retain their texture and flavor.