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Make the crust: In a food processor, pulse the dry ingredients a few times to combine. Place the butter slices over the top. In a small pitcher, combine the ice water and buttermilk. While pulsing the processor, pour in the liquid in a slow, steady stream. Remove the lid and squeeze the dough; it should have pea-size butter pieces, hold together, and feel moist but not sticky. If it feels dry, add a teaspoon or two more ice water and pulse quickly to combine until the dough is moistened enough to hold together when squeezed. Place a sheet of plastic wrap or wax paper on a clean work surface. Gather the dough into a ball, place it on the plastic wrap or wax paper, flatten into a disk, wrap tightly, and chill until firm, 30 to 60 minutes or up to 1 day.
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Dust a work surface lightly with oat flour and roll out the dough into a rough rectangle about 1/4-inch-thick, lifting and turning the dough, dusting the work surface to keep it from sticking, flipping it over, and removing excess flour with a pastry brush. (Alternatively, dust two pieces of parchment paper with oat flour and roll the dough between them to prevent sticking.) Fold the dough into thirds, as though folding a letter, then fold it in thirds again the other way. Gently press to flatten slightly, rewrap in plastic wrap or wax paper, and chill again, 30 to 60 minutes. Repeat the rolling and folding process once more and chill again until firm, 30 to 60 minutes.
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Prepare the vegetables: Place the leeks in a bowl, cover with cool water, separate the rings, and swish to remove any dirt. In a Dutch oven or large soup pot over medium-high heat, warm the oil. Using a slotted spoon, transfer the leeks to the pot. Add the sliced garlic and cook, stirring frequently, until the leeks begin to soften, about 3 minutes. Add the carrots, fennel, and potatoes and cook, stirring occasionally, 5 minutes longer. Add the mushrooms and 1/4 teaspoon salt and cook, stirring occasionally, 5 minutes longer. Add the vegetable stock, bring to a simmer, then reduce the heat and simmer, stirring occasionally, until the vegetables are firm-tender, 5 to 10 minutes longer. Remove from the heat.
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Meanwhile, make the béchamel: In a saucepan over medium heat, melt the butter. Whisk in the rice flour and cook, whisking, until bubbles form. Whisk in the milk, peppercorns, thyme, bay leaf, and salt and cook, whisking constantly, until the béchamel is simmering and has thickened to the consistency of yogurt. Pour the béchamel through a medium-mesh sieve directly onto the cooked vegetables. Stir in the lemon zest and juice and the parsley and season to taste with salt and pepper.
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Position a rack in the upper third of the oven and preheat to 400ºF. Line a round baking dish that is 10 to 11 inches in diameter and 2 inches high (or the equivalent) with parchment paper and place on a rimmed baking sheet.
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Pour the vegetable filling into the pan in an even layer. Dust a work surface lightly with oat flour. Place the chilled dough on the work surface and roll into a round 12 inches in diameter. Drape the dough over the top of the baking dish and trim the edge to overhang by about 1/2 inch. Cut 8 slits in the top of the dough to allow steam to escape and brush all over with the beaten egg.
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Bake the potpie until the crust is golden brown and the filling is bubbling, 40 to 50 minutes. Let cool slightly before serving.