In a large mixing bowl, whisk together the flour, cocoa powder, sugar, and salt.
Add the cold butter to the bowl and use your fingers or a pastry cutter to cut it into the dry ingredients until the mixture resembles coarse crumbs.
Gradually add the ice water, a tablespoon at a time, and mix until the dough comes together. Shape the dough into a disk, wrap it in plastic wrap, and refrigerate for at least 30 minutes.
Preheat the oven to 400°F (200°C).
Roll out the chilled dough on a lightly floured surface to a circle about 12 inches in diameter. Transfer the dough to a baking sheet lined with parchment paper.
Sprinkle the chopped chocolate over the center of the dough, leaving a 2-inch border around the edges. Top the chocolate with the raspberries.
Fold the edges of the dough over the filling, pleating as necessary. Press gently to seal any cracks.
Bake the galette in the preheated oven for 25-30 minutes, or until the crust is golden brown.
Remove from the oven and allow to cool for a few minutes. Dust with powdered sugar before serving.