Add flour and cold butter in a large bowl and using your fingers press down the butter cubes in such a way that butter and flour are well combined.
Add brown sugar and salt to the mixture & mix well. Add a little cold water to it and just make sure the mixture forms a dough shape. Don’t knead it, just combine everything and freeze it for 30 minutes.
Cut apples into thin slices. Add sugar, salt & lemon juice to it and keep aside.
In a small pan, add butter and brown sugar. Cook it until you see the color of butter has changed to brown. Keep the flame low.
Once the butter cools down, add it to the apple slices and mix well.
On a lightly floured surface, roll out the dough into a round shape about ⅛-inch (3 mm) thick. Roll the dough around the rolling pin and transfer it to the prepared baking sheet.
Now arrange the apple slices on the prepared sheet (shown in the image).
Freeze it for another 20-25 minutes. Take out the Galette, brush some egg wash on the side, and sprinkle coarse sugar.
Bake at 400 degrees F for 20-25 minutes.
Serve with vanilla ice cream.