All-Butter Pie Crust

1. Whisk 180 g flour, 1 tablespoon sugar, and 1/2 teaspoon kosher salt together in a large bowl. Add 156 g cold butter and use a pastry cutter to cut it into the flour until the mixture contains irregular pieces of butter ranging from coarse crumbs to about pea-size.
2. Add up to 1/4 cup ice water, 1 tablespoon at a time, gently mixing with a silicone spatula after each addition. Add only enough water for the dough to hold together when you squeeze a handful. The dough should look rough and shaggy, not wet or smooth.
3. Turn the dough onto a lightly floured work surface and gently bring it together with your hands. Avoid kneading or working the dough more than necessary. Shape the dough into a disc about 1 inch thick, wrap tightly in plastic wrap, and refrigerate for at least 1 hour.
4. Repeat Steps 1–3 with the remaining flour, sugar, salt, butter, and ice water to make the second crust. Refrigerate both discs until ready to roll.

Filling and Glaze

1. Melt the butter in a large Dutch oven or heavy-bottomed pot over medium heat. Continue cooking as the butter foams and the milk solids begin to brown. Cook, stirring frequently and watching closely, until the milk solids are golden brown and the butter smells nutty.
2. Peel, core, and cut the apples into ¼-inch-thick slices. Add the apples, brown sugar, granulated sugar, lemon juice, cinnamon, nutmeg, allspice, cloves, and salt directly to the browned butter. Gently toss to combine.
3. Cook the apples over medium heat, stirring gently and occasionally, until they begin to soften and release their juices, about 8–10 minutes. The apples should become flexible but remain intact, with a slightly firm center.
4. Transfer the apples to a large bowl using a slotted spoon, leaving the butter and released juices in the pot. Set the apples aside to cool.
5. Add the apple cider to the juices in the pot. Bring to a gentle boil and cook, stirring occasionally, until the liquid reduces and concentrates.
6. Whisk the tapioca starch with 2 tablespoons cold water until smooth. Slowly stir the slurry into the reduced liquid and cook briefly, stirring constantly, until the glaze thickens and becomes clear and glossy. Remove from the heat and stir in the vanilla.
7. Return the apples to the pot and gently fold until every slice is evenly coated with the glaze. The glaze should cling to the apples without pooling heavily in the bottom of the pot.
8. Transfer the filling to a large bowl or rimmed baking sheet and allow it to cool completely before assembling the pie.

Assemble and Bake the Pie

1. Preheat the oven to 425°F. Position a rack in the lower third of the oven.
2. Remove one dough disc from the refrigerator and let it stand at room temperature for 5–10 minutes, just until pliable enough to roll without cracking. On a lightly floured surface, roll the dough into a circle about 12 inches in diameter and about 3/16-1/4 inch thick.
3. Gently roll the dough around the rolling pin and unroll it over a 9-inch pie plate. Ease the dough into the bottom and sides of the plate without stretching it, leaving the excess dough extending beyond the edge.
4. Spoon the completely cooled apple filling into the crust, distributing the apples evenly and mounding them slightly toward the center. There’s no need to compress the apples or force more filling into the pie.
5. Roll the second dough disc into a circle about 12 inches in diameter and approximately 3/16 to 1/4 inch thick. Gently roll the dough around the rolling pin and unroll it over the filling.
6. Trim the top and bottom crusts to about 1 inch beyond the edge of the pie plate. Fold the edges under together, press firmly to seal, then crimp the perimeter with a fork. Cut several vents in the top crust.
7. Whisk the egg with 1 tablespoon water. Lightly brush the top crust with the egg wash and sprinkle with coarse sugar, if desired.
8. Bake at 425°F for 20 minutes. Reduce the oven temperature to 375°F and continue baking for 40–50 minutes, until the crust is deeply golden and the filling is bubbling through the vents. Shield the edges loosely with foil if they brown too quickly.
9. Transfer the pie to a wire rack and cool completely, at least 4 hours, before slicing.