Whisk together the flours, salt, lemon zest and brown sugar. Cut in the butter, using a pastry cutter, two forks or a food processor fitted with a dough blade until the mixture is crumbly. Drizzle in 3 tablespoons of water, stirring gently until everything is evenly moistened; add the final tablespoon of water if necessary to make a cohesive dough.
Form the dough into a round ball. Wrap in plastic wrap or place in a quart-size bag and set in the fridge to rest for at least 30 minutes. This can be made a day in advance.
Make the Blueberry Filling
Place all ingredients for the filling in a large bowl and toss together to combine. Set aside.
Make the Galette
Preheat oven to 400 degrees F.
Roll the dough on a floured surface into a 15-inch round. If your dough is sticking at all, dust the surface with more flour. Line a baking sheet (preferably without sides; a round baking stone works well. If your baking sheet only has sides, flip it over and use the back). Transfer the dough by rolling it onto your rolling pin and then unrolling it onto the prepared pan.
Spread the blueberry filling in the center of the dough in a single layer. Lift the edges of the dough and fold them inward over the filling, pleating as you go. If desired, brush the beaten egg over top. Sprinkle the course sugar on top, if using.
Bake until the crust has browned, about 20 minutes. When done, remove the baking sheet from the oven and slide the galette off the parchment paper onto a cooling rack. Let cool for 10 minutes.
Make the Lemon Whipped Cream
While the galette is baking, place all ingredients for the lemon cream in the base of a stand mixer or bowl fitted with a hand mixer and whip until thick and creamy. Cut the galette into wedges and serve with the whipped cream.