LEEK, MUSHROOM AND GOAT CHEESE GALETTE

Steps:

• For the Dough: Process the flours, sugar, and salt in food processor until combined, 3 to 4 pulses. Add the butter and pulse until it forms pea-size pieces. In a small bowl, measure the ice water and add the vinegar. Drizzle it over the dry ingredients and pulse a couple of times, until the dough just starts to pull away from the sides of the processor. Do not overwork the dough (see note below).
• Transfer the mixture to the center of a large sheet of plastic wrap, press gently into a rough 4-inch square, and wrap tightly. Refrigerate for at least 30 minutes.Transfer the dough to a lightly floured work surface. Roll into an 11x8-inch rectangle with the short side of the rectangle parallel to the edge of your work surface. Using a bench scraper, bring the bottom third of the dough up, then fold the upper third over it, folding it like a business letter into an 8x4-inch rectangle. Turn the dough 90 degrees counterclockwise. Roll out the dough again into 11x8-inch rectangle and fold into thirds again. Turn the dough 90 degrees counterclockwise again and repeat rolling and folding into thirds. After the last fold, fold the dough in half to create a 4-inch square. Press the top of the dough gently to seal. Wrap the dough in plastic wrap and refrigerate for at least 30 minutes or up to 2 days.
• For the Filling: Clean the mushrooms, cut them into small pieces (about ½") and then dry-sauté (without any fat) them in a hot, 12" skillet for 5-6 minutes, stirring frequently. Remove the mushrooms from the skillet to a bowl and reserve. To the same skillet, heat the olive oil over medium heat. Add the leeks (white part and pale green part only) and the thyme, cover, and cook, stirring occasionally, until the leeks are tender and beginning to brown, 5 to 7 minutes. Transfer the leeks to the bowl with the mushrooms. Stir in the half and half (or cream) and the mustard. Season with salt and pepper to taste. Set aside.
• Adjust an oven rack to the lower middle position, place a pizza stone on the rack, and heat the oven to 400 °F. Remove the dough from the refrigerator and let stand at room temperature for 10 minutes. Roll out the dough on a generously floured work surface into a 14" circle about ⅛-inch thick. (Trim the edges as needed to form a rough circle.) Transfer the dough to a parchment paper-lined rimmed baking sheet. Using a fork, prick the dough a few times. Brush the top of the dough with 1 tsp. of olive oil.
• Spread half of the filling evenly over the dough, leaving a 2-inch border around the edge. Sprinkle with half of the goat cheese, cover with the remaining filling, and top with the remaining goat cheese. Drizzle the remaining 1 tsp. of oil over the filling. Grasp 1 edge of the dough and fold up the outer 2 inches over the filling. Repeat around the circumference of the dough, overlapping it every 2 to 3 inches; gently pinch the pleated dough to secure but do not press the dough into the filling. Brush the dough with the egg and sprinkle evenly with salt. Lower the oven temperature to 375 °F.
• Bake until the crust is deep golden brown and the filling is beginning to brown, 35 to 40 minutes. Cool the tart on the baking sheet on a wire rack for 10 minutes. Using an offset or wide metal spatula, loosen the tart from the parchment and carefully slide the tart off the parchment and onto a cutting board. Cut into wedges, and serve.