Pre-heat oven to 375℉.
Slice apple(s) into thin slices
In a large bowl, combine sliced apples, brown sugar, lemon juice, pure maple syrup, all purpose flour, and ground cinnamon. Mix well to evenly coat apples. Use hands to coat evenly if needed.
Roll out pie crust on a baking sheet lined with parchment paper. Place sliced apples (overlap and pack them!) onto the middle of the pie crust, leaving ~1 1/2 inch all around to fold over. Overlap the apple slices a little bit so you can pack in more of them. Do not dump the whole bowl of sliced apples onto the crust because we will be using the liquid from the apple mixture to drizzle onto the top of the galette.
Once apples are arranged onto the crust, fold over the sides of the pie crust. Drizzle leftover liquid from apple mixture to the top of the sliced apples.
Whisk an egg in a small bowl. Using a brush, brush the folded-over sides with egg wash. Then sprinkle with coarse sugar.
Bake for 40 minutes, or until crust is golden brown and apples are slightly tender. Apples will not be completely soft, but partially tender and partially crunchy.
Let galette sit for 10 minutes. Serve with vanilla ice cream and enjoy!