1. Preheat the oven to 375°F.

2. Rinse and drain the chard. Remove the stems trim and discard the woody bottoms, chop the rest: and set aside. Coarsely chop the leaves.

3. Heat 2 tablespoons of the oil in a skillet over low heat. Add the onion and sauté until wilted, about 5 minutes. Stir in the chard stems and cook 3 minutes.

4. Stir in the chard leaves, and cook 3 minutes more. Drain off the excess liquid, and transfer the mixture to a bowl. Season with the salt and pepper. Stir in the Jarlsberg, 1 tablespoon of the crumbs, and the Parmesan. Set aside.

5. Stir the butter and remaining 2 tablespoons olive oil together in a small bowl.

6. Open 1 sheet of phyllo on a work surface. Brush it with some of the butter and oil mixture. Sprinkle with 1 teaspoon of the crumbs.

7. Top with 4 more sheets of phyllo, brushing each with butter and oil and sprinkling each with crumbs. Top with the remaining sheet, and brush it with butter and oil.

8. Spoon the filling along one short end of the phyllo, leaving about 1½ inches empty on each side. Fold the long sides in, overlapping the filling by 1½ inches, to enclose the ends of the filling.

9. Roll the phyllo and filling over onto itself to form a strudel roll. Place it on a baking sheet seam side down and brush the top with any remaining butter and oil. Bake until deep golden, 25 minutes. Let the strudel stand for 5 minutes before slicing and serving.