Position a rack in the center of the oven and preheat the oven to 350 degrees F.
Liberally butter a 9-inch tart pan with a removable base.
For the crust: In a food processor, combine the flours, parsley, thyme and 1/2 teaspoon salt 1/4 teaspoon pepper. Pulse to combine. Add the butter and pulse until the mixture forms a coarse meal. With the motor running, gradually add the ice water and process until the mixture forms a ball. Form the dough into a disc and wrap in plastic wrap. Refrigerate for 20 minutes.
On a lightly floured work surface, roll out the dough into a 10-inch round. Place the dough in the prepared pan and trim any excess dough from the top of the pan. Using a fork, prick the dough all over and bake for 12 minutes. Let the crust cool for 15 minutes.
For the filling: In a medium skillet, heat the olive oil over medium-high heat. Add the leeks and cook, stirring frequently, until softened, about 3 minutes. Add the arugula and cook until wilted, about 2 minutes. Spoon the leek mixture over the crust. Sprinkle the goat cheese and smoked salmon on top.
In a medium bowl, whisk together the eggs, 1 teaspoon salt and 1/2 teaspoon pepper until frothy. Pour the egg mixture over the filling. Place the tart pan on a baking sheet and bake until the filling has set and the cheese begins to brown, 35 to 40 minutes. Cool for 30 minutes, then remove the sides and base of the tart pan.