Instructions

for the crust

Process flour, sugar, salt, mustard, and cayenne in food processor until combined, about 5 seconds. Scatter cheddar and butter over top and pulse until butter is size of large peas, about 10 pulses.
Pour half of ice water over flour mixture and pulse until incorporated, about 3 pulses. Repeat with remaining ice water. Pinch dough with your fingers; if dough feels dry and does not hold together, sprinkle 1 to 2 tablespoons extra ice water over mixture and pulse until dough forms large clumps and no dry flour remains, 3 to 5 pulses.
Divide dough in half and form each half into 4‑inch disk. Wrap disks tightly in plastic wrap and refrigerate for 1 hour. Let chilled dough sit on counter to soften slightly, about 10 minutes, before rolling. (Wrapped dough can be refrigerated for up to 2 days or frozen for up to 1 month. If frozen, let dough thaw completely on counter before rolling.)

for the filling

Stir apples, granulated sugar, brown sugar, lemon zest, salt, and cinnamon together in Dutch oven. Cover and cook over medium heat, stirring frequently, until apples are just tender but still hold their shape, 10 to 15 minutes. Off heat, stir in lemon juice. Spread apple mixture on rimmed baking sheet and let cool completely, about 30 minutes. (Filling can be refrigerated for up to 24 hours.)
Roll 1 disk of dough into 12‑inch circle between 2 sheets of parchment paper or plastic. Loosely roll dough around rolling pin and gently unroll it onto 9‑inch pie plate, letting excess dough hang over edge. Ease dough into plate by gently lifting edge of dough with your hand while pressing into plate bottom with your other hand. Trim overhang to 1/2 inch beyond lip of pie plate. Wrap dough-lined pie plate loosely in plastic and refrigerate until dough is firm, about 15 minutes.
Adjust oven rack to lowest position and heat oven to 425 degrees. Fill pie shell with apple mixture. Roll other disk of dough into 12‑inch circle between 2 sheets of parchment or plastic. Loosely roll dough around rolling pin and gently unroll it onto filling.
Trim overhang to 1/2 inch beyond lip of pie plate. Pinch edges of top and bottom crusts firmly together. Tuck overhang under itself; folded edge should be flush with edge of pie plate. Crimp dough around edge of pie plate using your fingers. Cut four 2-inch slits in top of dough.
Set pie on foil or parchment-lined baking sheet and bake for 20 minutes. Reduce oven temperature to 375 degrees and continue to bake until crust is deep golden brown and filling is bubbling, 35 to 45 minutes. Transfer pie to wire rack and let cool for at least 1 1/2 hours. Serve.