Combine 2 cups of the pastry flour, rye flour, 1 teaspoon of the cinnamon and salt in a food processor and pulse until combined.

Add butter and pulse until the size of small peas.

Drizzle in 6 tablespoons ice-cold water and pulse, scraping down the sides halfway through. (If using coconut oil, you may need to add an additional 2 to 3 tablespoons ice-cold water to achieve a soft dough that sticks together.)

Press into two 5-inch disks.

Wrap each in plastic wrap and refrigerate until cold, 1 to 2 hours.

Preheat the oven to 350F.

Line a large rimmed baking sheet with parchment paper.

In a small bowl, beat egg with 1 tablespoon water to make an egg wash.

On a floured surface, roll out one dough disk into a 10x14-inch rectangle.

Transfer to the prepared baking sheet.

Refrigerate while you repeat with remaining dough disk.

Brush outer edge of dough on the baking sheet with egg wash.

Spread apples and accumulated juices over dough, leaving a 1 1/2-inch border.

Lay second piece of dough on top. Fold over and crimp outside edge.

Brush top crust with egg wash and cut a few small slits or circles in the top.

Bake until crust is golden brown and filling is bubbly and tender, about 50 minutes.

Cool on a wire rack until warm or at room temperature.

Cut into pieces and serve.