This savory tart brings together meltingly tender leeks, soft ripened and aged cheeses, and a crisp, golden buttery backdrop of store-bought puff pastry.
If using baby leeks, halve lengthwise and trim to about 3 inches long. If using regular leeks, cut crosswise into 3-inch pieces; halve each piece lengthwise, then cut into 3/8-inch-thick strips (about 5 cups). Rinse well, and drain; set aside.
Melt butter with oil in a medium saute pan over medium heat. Add leeks and 1/4 teaspoon salt; cook, stirring occasionally, 5 minutes. Reduce heat to medium-low; cover, and cook, stirring occasionally, until leeks are tender but not browned, about 15 minutes. Stir in thyme. Leeks can be refrigerated in an airtight container up to 1 day; bring to room temperature before assembling tart.
Cut or roll out pastry to a 6-by-14-inch rectangle; place on a parchment-lined baking sheet (reserve remaining pastry for another use). Score a 3/4-inch border. Brush with egg wash; sprinkle with Parmesan. Refrigerate 30 minutes.
Preheat oven to 375 degrees. Bake pastry until golden, 10 to 15 minutes. Remove from oven, and press center area with a metal spatula. Arrange leeks end to end in rows within border of pastry. Scatter olives over leeks. Bake until crust is golden brown, about 10 minutes. If bottom is soft, bake 3 to 5 minutes more.
Remove tart from oven, and arrange soft cheese over top. Using an offset spatula, slide tart onto a wire rack; let cool slightly. Cut into pieces; serve warm or at room temperature (tart can stand at room temperature up to 1 hour).