Using a high speed food processor ground the coconut to a fine meal. In a large bowl combine the ground coconut, the flour and 3 tbsp brown sugar. Add butter cubes, then rub in with your fingers until the mixture looks like fine crumbs. Add the ice water and combine everything to a dough. Place in plastic wrap and let it cool in the fridge for about 60 minutes.
Preheat the oven to 180°C.
Peel, quarter and core pineapple and cut into slices.
When the dough is ready roll it out on a lightly floured surface (or directly on the parchment paper) to about 1/4 inch thickness. Transfer to a baking sheet lined with parchment paper.
Arrange pineapple slices onto dough leaving a 3 inch border around the edges. Fold edges over, overlapping slightly. Brush dough with egg wash and sprinkle with remaining brown sugar.
Bake the galette for 40-55 minutes or until crust is golden. Serve warm for example with coconut ice-cream.