Combine the flour, sugar, and salt in a large bowl. Using the pastry blender cut in the butter until the dough has a consistency of sand with larger size pebbles. If you are using a food processor add all of the ingredients but the water to the bowl and blend until you reach the desired consistency.
Add the water 1 tablespoon at a time until all of the flour is incorporated and doesn't crumble away.
Wrap in cling film and set in the refrigerator for at least 30 min.
Making the filling
Over medium high heat in a saucepan heat the butter until the milk solids turn a dark rich brown color. Remove from the heat and set aside to cool.
Using a knife or mandoline slice the apple thinly into discs and then cut the discs in half and remove the core portion. Place in a bowl of water to keep from turning brown.
Add the butter to the brown sugar and vanilla. Mix thoroughly.
Drain the water from the apples in colander and shake to remove excess water. Add them back to the bowl and mix in the butter mixture. Use your hands here to be able to spread the mixture without breaking the apples.
Assembly
Preheat oven to 350°F or gas mark 4.
Remove the dough ball from the freezer and roll out to an 18 inch disk. Place the dough on the baking sheet you are planning on baking the galette on.
Starting from the outside, leaving a 1 1/2" border around the edge, create a circle of overlapping apple slices. Continue to arrange the apples in concentric circles so they overlap slightly.
Fold the edge nearest to you towards the center. Rotate sheet plan slightly and repeat, until all edges are folded towards the apples.
Brush with the beaten egg and sprinkle with turbinado sugar and bake for about 40 min or until crust is golden brown. Cool completely.