Roll out pastry to fit into a rectangle tart pan or free form pastry on a large baking sheet. Put pastry in the tart pan and fit it up the edges. Using a sharp knife score the edges around the pan. Dock the bottom of the pastry with a fork liberally. Refrigerate for 30 minutes.
Preheat oven to 400 degrees.
Meanwhile, slice leek white and light green parts in two lengthwise. Cut into 1/4 inch slices. Put leeks into a large bowl of water and swoosh around to remove any dirt. Remove to a paper towel and pat dry.
Heat 1 TBS oil and butter in a large pan over medium heat. Add leek and cook for 20 minutes until soft and slightly golden. Take off heat and reserve.
Put puffed pastry in oven and cook for 15 minutes.
Meanwhile, trim asparagus to fit in the tart pan.