Preheat oven to 375 degrees. On a lightly floured work surface, roll pastry to a 10-by-14-inch rectangle. Halve lengthwise into two 5-by-14-inch rectangles. Transfer to a baking sheet lined with parchment paper.
With a paring knife, lightly score each rectangle 1/2 inch from edges, creating a border; prick pastry inside border all over with a fork. Refrigerate for 15 minutes, then bake until golden brown, 18 to 20 minutes. (To store, keep crusts at room temperature, up to 1 day.)
In a large skillet, heat butter over medium. Add leeks; season with salt and pepper, and stir. Cover; cook until wilted, about 5 minutes. Uncover; cook until tender, 10 to 12 minutes. Spoon leeks onto crusts, cut tarts into wedges, and serve.