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Preheat the oven to 400°F with a rack in the center position.
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Scatter the walnuts and 3 tablespoons (16g) of the oats on a baking sheet and toast until the walnuts are golden brown and fragrant, 7 to 10 minutes, tossing halfway through. Set the pan aside and let the nuts and oats cool. Leave the oven on for parbaking the crust.
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To roll out the pastry dough: Remove the dough from the refrigerator and unwrap it. You will need 2/3 of the total dough for this slab pie, so use a knife or bench knife to slice off about 1/3 of the dough. Wrap the smaller piece and return to the refrigerator or freezer for another use.
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Let the dough sit at room temperature for a minute or two to soften slightly, then place it on a lightly floured surface. Use a rolling pin to beat the dough all over the surface to make it more pliable. Dust more flour underneath and on top of the dough, then roll it out, dusting with more flour as needed, into a rectangle measuring about 15" x 12".
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Roll the pastry onto the rolling pin, then unroll it onto a 13" x 9" baking sheet (quarter sheet pan), centering it so you have equal overhang along all 4 sides. Firmly press the pastry into the bottom and against the sides of the pan, ensuring contact everywhere and taking care not to stretch it. Use scissors to trim the edges of the pastry, leaving a 1/2" overhang all the way around (save the scraps for another use or coat with cinnamon sugar, bake, and enjoy as a baker’s snack). Tuck the overhanging dough underneath itself so you have a thick border of pastry resting on the rim of the pan along all sides. Using your thumb on one hand and your thumb and forefinger on the other, crimp the border, flouring your fingers if needed to prevent sticking.
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To parbake the pastry dough: Freeze the pan until the dough is very firm, 10 to 15 minutes, then prick (dock) the dough in several places across the bottom of the pan with a fork to prevent it from puffing up as it bakes. Line the pan with a double layer of foil, pressing the pieces into the bottom and up the sides and leaving several inches of overhang on all sides. Fold the overhang down and over the crimped edge of the dough to cover. (This will prevent the edges from over-browning.) Fill the pan with pie weights, dried beans, rice, or granulated sugar and spread in an even layer, then place the lined pan on a larger baking sheet.
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Bake the crust for 25 to 30 minutes, until the edge is set and starting to turn golden when you peek underneath the foil, then remove it from the oven. Reduce the temperature to 325°F.
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Carefully use the overhanging foil to lift the pie weights out of the crust and set them aside. Return the baking sheet to the oven and bake for 25 to 30 minutes longer, until the crust is golden brown across the bottom, then remove it from the oven. While the crust is baking, prepare the filling.
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To make the filling: In a small saucepan, combine the butter and the remaining 1/2 cup (45g) oats and cook over medium heat, stirring occasionally with a heatproof flexible spatula, until the butter is melted. Increase the heat to medium-high and bring the mixture to a boil, stirring constantly. Continue to cook, stirring all the while, until the oats are deep golden brown and the butter is foaming and you see tiny brown specks swimming in the foam, 10 to 15 minutes. Remove the saucepan from the heat.
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Slowly add the cream to the saucepan, stirring constantly (be careful, it will sputter aggressively at first). Once all the cream is added, bring the mixture to a simmer over medium-low heat and cook, stirring constantly, until it’s thickened to the consistency of a loose porridge, about 2 minutes. Remove the saucepan from the heat and set aside.
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In a large bowl, whisk together the whole eggs, yolks, brown sugar, maple syrup, vanilla, salt, and cinnamon until the eggs are broken up, then whisk vigorously until the mixture is completely smooth and streak-free, 1 to 2 minutes. Whisking constantly, slowly pour in the hot cream mixture. Set the filling aside until the crust is finished parbaking.
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To assemble and bake the slab pie: Scatter the toasted walnuts and oats across the bottom of the hot parbaked crust in an even layer. Whisk the filling again and pour it into the crust, evenly distributing the cooked oats that have settled to the bottom of the bowl (the heat in the crust will set the bottom layer of filling quickly, preventing sogginess, and will help the pie cook faster). Transfer the baking sheet to the oven and bake until the filling is slightly puffed and the center is firm to the touch, 22 to 28 minutes. Transfer the pie to a wire rack to cool completely.
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Storage instructions: Store leftover walnut and oat pie, covered loosely at room temperature, for up to 4 days. The crust will soften over time.
