How to Make It
Preheat oven to 400°F.
Prepare the crust: Roll the pie dough to 1⁄8-inch thickness, and transfer to a 9-inch tart pan with a removable bottom. Press dough into bottom and up sides of pan, and trim excess dough around edges. Line bottom of dough with aluminum foil (or parchment paper), and fill with pie weights or dried beans. Bake 5 minutes. Remove pie weights and foil, and prick bottom of pastry evenly with a fork. Return to oven; bake until pastry is light golden brown, an additional 8 to 10 minutes. Transfer pan to a wire rack; cool crust completely, about 20 minutes. Reduce oven temperature to 350°F.
Meanwhile, prepare the filling: Set aside 6 or 7 whole asparagus spears, and cut remaining asparagus into 1⁄2-inch pieces. Melt butter in a skillet over medium-high. Add leek, and cook, stirring often, until tender, about 5 minutes. Stir in asparagus pieces, and cook, stirring often, until bright green, about 1 minute. Remove skillet from heat; cool vegetable mixture 5 minutes.
Whisk together eggs, cream, chopped parsley, salt, and pepper in a medium bowl until well combined. Transfer cooled crust to a baking sheet. Spoon vegetable mixture over the bottom of the crust, and sprinkle evenly with crumbled goat cheese. Pour the egg mixture over the vegetable-goat cheese mixture. Arrange the reserved whole asparagus spears on top.
Bake quiche at 350°F until center is just set, 50 to 55 minutes, shielding crust with aluminum foil after 10 minutes, if needed, to prevent excess browning. Transfer to a wire rack, and cool at least 15 minutes. Remove quiche from pan, and garnish with parsley leaves before serving.