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Step 1
In the bowl of a food processor, combine the flour, sugar, and salt. Pulse in the butter until it resembles pea-sized crumbs. Don’t over-process. In a small bowl, whisk together the egg yolkd and vanilla. Pulse the egg yolk mixture into the flour just until combined. Add the water and pulse to combine. Don’t process it to the point of it coming together into a dough. The mixture should still be shaggy but should clump together when you squeeze a bit of the mixture together in between your fingers. If it’s still dry add another teaspoon or so of ice water and then pulse to combine. Dump the mixture out onto a clean work surface and bring the dough together into a ball. Flatten it out into a disk, wrap it is plastic wrap, and refrigerate for at least 30 minutes but preferably 2 hours.
Step 2
When ready to prepare your pie, roll the dough out onto a lightly floured work surface. Roll out the dough to fit into a 9” tart pan with a removable bottom. The dough should be about 2” larger than the pan on all sides. Roll the dough onto your lightly floured rolling pin and gently unroll it into your tart pan. Gently fit the dough into the edges of your pan and use a paring knife or kitchen scissors to trim any dough that extends over 1” the lip of the pan. Press the dough gently into the sides of the pan and use any leftover dough to reinforce the sides where needed. Put the pan in the freezer to set up for 30 minutes while you preheat the oven to 375 degrees.
Step 3
When ready to bake, prick the bottom of the tart dough with a fork a few times. Use a sheet of parchment to line the pastry dough inside the pan and f ill the tart pan with pie weights (you can also use dried beans or dried rice). Bake in the preheated oven for 15 minutes then remove the parchment and weights from the tart pan. Gently brush the crust with a thin layer of the egg white and bake for 5 more minutes.
Step 4
In the meantime, prep your filling: Cube the butter and add to a medium heavy-bottomed saucepan to being browning it. Place the pan on medium heat and stir gently with a whisk regularly to allow the butter to melt evenly. Once melted, keep stirring regularly to allow the butter to cook, sizzle, and foam evenly. You’ll begin to notice golden flecks appearing at the bottom of the pan and the butter will become fragrant. When there are amber-colored flecks throughout the butter mixture your butter is browned! Don’t let it burn! Immediately remove it from the heat and pour into a heat-safe mixing bowl. Stir in the sugar. Stir in the egg and vanilla extract and then fold in the flour. Pour the mixture into the par-baked pastry shell and spread to even it out.
Step 5
Prepare the apples by tossing together the sliced apples, brown sugar, lemon juice, and cinnamon. Arrange the slices on top of the brown butter filling according to your preferences. Bake in the preheated oven for an additional 35 minutes or until the crust is golden and the filling it cooked underneath. Serve cooled slices with ice cream or whipped cream!