Preheat the oven to 350°F. Add the flour, salt, and butter to your food processor and run until the mixture is crumbly. Drizzle in the ice water while the machine is running until the dough forms a ball.
Shape the ball into a disc and cover it with plastic wrap, then refrigerate for 30 minutes. Cut a sheet of parchment paper to the size of your baking tray, ensuring it can contain the galette.
Use a rolling pin to roll out the dough so that it is ¼-inch thick. Lay the dough onto the parchment paper. Place the blueberries on top of the dough, leaving about a 4-inch pastry border around the fruit. Sprinkle the blueberries with the lemon juice and lemon zest.
Gently fold the edges of the pastry in towards the center, overlapping a bit to form a circle. Whisk the egg and brush it onto the top of the pastry.
Sprinkle the brown sugar over the pastry and bake for 15–20 minutes, or until golden brown on top and crisp on the bottom. Let rest for a few minutes before enjoying so the filling can set.