In a large bowl, whisk together the flour, cocoa powder, granulated sugar, and salt.
Add the cold butter to the bowl and use your fingers or a pastry cutter to cut the butter into the dry ingredients until the mixture resembles coarse crumbs.
Drizzle the ice water over the mixture and gently mix until the dough comes together. Shape the dough into a disk, wrap in plastic wrap, and refrigerate for 30 minutes.
Preheat the oven to 400°F (200°C). Line a baking sheet with parchment paper.
On a lightly floured surface, roll out the chilled dough into a 12-inch circle. Transfer the dough to the prepared baking sheet.
In a small bowl, combine the almond meal, brown sugar, and ground cinnamon. Sprinkle the mixture evenly over the dough, leaving a 2-inch border.
Arrange the pear slices in an overlapping pattern over the almond mixture. Sprinkle the chocolate chips over the pears.
Fold the edges of the dough over the filling, pleating as necessary. Brush the edges of the dough with the beaten egg wash.
Bake for 20-25 minutes, or until the crust is golden brown and the pears are tender.
Remove from the oven and let cool slightly. Dust with powdered sugar before serving.