Preheat oven to 400F.
Heat oil in a skillet over medium-high heat. Add spinach and leeks. Cook until leeks have caramelized and spinach is wilted. Set aside.
On a floured surface, roll out puff pastry dough to 1/8-inch-thick. Cut into 4 equal rectangles.
Working with one rectangle at a time, add 2 tablespoons jack cheese 1/2-inch from the bottom (width) of the rectangle. Top with 1/4 cup chorizo, 1/4 of spinach mixture, and again with 2 tablespoons cheese.
Brush around filling with melted butter. Fold top down to the bottom so the ends touch, then press down to seal edges. Brush top of strudel with butter and place on a baking sheet fitted with a silicone baking mat.
Repeat process with remaining dough rectangles and filling ingredients. Bake until golden brown, about 30 minutes. Serve hot.