Many free-form vegetable tart recipes simply borrow a standard pastry dough intended for fruit, but vegetables are more prone to leaking liquid into the crust or falling apart when the tart is sliced. We needed a crust that was extra-sturdy and boasted a complex flavor of its own. We also wanted a robust-tasting filling featuring the classic combination of meaty mushrooms and sweet leeks. To give the crust earthy flavor and a hearty crumb, we added in some whole-wheat flour. To keep the dough tender, we took a hands-off approach to mixing; we just barely mixed the dry and wet ingredients together, and then rested the dough briefly before rolling it out. To punch up its flaky texture and create more structure, we gave the dough a series of folds to create numerous interlocking layers. To remove moisture from the vegetables, we microwaved and drained the mushrooms and browned the leeks on the stovetop. Finally, we made a rich binder with crème fraîche, Dijon mustard, and crumbled Gorgonzola. An equal amount of rye flour can be substituted for the whole-wheat flour. Cutting a few small holes in the dough prevents it from lifting off the pan as it bakes. If you do not have a baking stone, you can use a preheated rimless (or inverted) baking sheet.
1. For the dough: Pulse all-purpose flour, whole-wheat flour, sugar, and salt in food processor until combined, 2 to 3 pulses. Add butter and pulse until pea-size pieces form, about 10 pulses. Transfer mixture to medium bowl.
2. Sprinkle water and vinegar over mixture. With rubber spatula, use folding motion to mix until loose, shaggy mass forms with some dry flour remaining (do not overwork). Transfer mixture to center of large sheet of plastic wrap, press gently into rough 4-inch square, and wrap tightly. Refrigerate for at least 45 minutes.
3. Transfer dough to lightly floured counter. Roll into 11 by 8-inch rectangle, with short side of rectangle parallel to edge of counter. Using bench scraper, bring bottom third of dough up over middle third, then fold upper third over it, folding like business letter into 8 by 4-inch rectangle. Turn dough 90 degrees counterclockwise. Roll out dough again into 11 by 8-inch rectangle and fold into thirds again. Turn dough 90 degrees counterclockwise and repeat rolling and folding into thirds. After last fold, fold dough in half to create 4-inch square. Press top of dough gently to seal. Wrap in plastic wrap and refrigerate for at least 45 minutes or up to 2 days.
4. For the filling: Microwave mushrooms in covered bowl until just tender, 3 to 5 minutes. Transfer to colander to drain, then return to bowl. Meanwhile, heat 1 tablespoon oil in 12-inch skillet over medium heat until shimmering. Add leeks and thyme, cover, and cook, stirring occasionally, until leeks are tender and beginning to brown, 5 to 7 minutes. Transfer to bowl with mushrooms. Stir in crème fraîche and mustard and season with salt and pepper to taste. Set aside.
5. Adjust oven rack to lower-middle position, place baking stone on rack, and heat oven to 400 degrees. Remove dough from refrigerator and let stand at room temperature for 15 to 20 minutes. Roll out on generously floured (up to 1/4 cup) counter to 14-inch circle about 1/8 inch thick. (Trim edges as needed to form rough circle.) Transfer dough to parchment paper–lined rimmed baking sheet. With tip of paring knife, cut five 1/4-inch circles in dough (1 at center and 4 evenly spaced midway from center to edge of dough). Brush top of dough with 1 teaspoon oil.
6. Spread half of filling evenly over dough, leaving 2-inch border around edge. Sprinkle with half of Gorgonzola, cover with remaining filling, and top with remaining Gorgonzola. Drizzle remaining 1 teaspoon oil over filling. Grasp 1 edge of dough and fold up outer 2 inches over filling. Repeat around circumference of tart, overlapping dough every 2 to 3 inches; gently pinch pleated dough to secure but do not press dough into filling. Brush dough with egg and sprinkle evenly with kosher salt.
7. Lower oven temperature to 375 degrees. Bake until crust is deep golden brown and filling is beginning to brown, 35 to 45 minutes, rotating sheet halfway through baking. Cool tart on baking sheet on wire rack for 10 minutes. Using offset or wide metal spatula, loosen tart from parchment and carefully slide tart off parchment and onto cutting board. Sprinkle with parsley, cut into wedges, and serve.