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1
If using baby leeks, halve lengthwise and trim to about 3 inches long.
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2
If using large leeks, cut crosswise into 3-inch pieces; halve each piece lengthwise, then cut into 1/2-inch-thick strips (about 5 cups).
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3
Rinse well to remove any grit, and drain.
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4
Melt butter with oil in a medium saute pan over medium heat.
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5
Add leeks and salt; cook, stirring occasionally, 5 minutes.
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6
Reduce heat to medium low; cover, and cook, stirring occasionally, until leeks are tender but not browned, about 15 minutes.
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7
Stir in thyme.
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8
Leeks can be cooled completely and refrigerated in an airtight container up to 1 day; bring to room temperature before assembling tart.
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9
Roll out or trim dough to a 14-by-6-inch rectangle.
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10
(If necessary, overlap edges of two smaller pieces to form a large rectangle; brush overlap with water to seal, then roll out.)
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11
Place on a parchment-lined baking sheet (reserve remaining dough for another use).
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12
Score a 3/4-inch border on all sides (do not cut all the way through).
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13
Brush border with egg wash; sprinkle with grated cheese.
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14
Refrigerate 30 minutes.
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15
Preheat oven to 375F.
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16
Bake until golden, 10 to 15 minutes.
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17
Using an offset spatula, press down on center of shell (leave edges raised).
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18
Arrange leeks end to end in rows within border of crust.
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19
Scatter olives over leeks.
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20
Bake until crust is golden brown, about 10 minutes more.
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21
Use a wide spatula to lift to check bottom of crust; if its still soft, bake 3 to 5 minutes more.
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22
Arrange soft cheese over top.
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23
Using a large offset spatula, slide tart onto a wire rack; let cool slightly.
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24
Cut crosswise into pieces; serve warm or at room temperature.
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25
Tart can be kept at room temperature up to 1 hour before serving.
