Preheat the oven to 375ºF and line a baking sheet with parchment paper.
Roll out your pie crust into a 10-inch circle that is about ⅛-inch thick and place it on a parchment-lined large plate. Place the pie crust in the fridge for 15 minutes to firm up.
While pie crust is firming up, place the walnuts, flour, 1 teaspoon brown sugar, ½ teaspoon cinnamon and ¼ teaspoon salt into a food processor. Process the ingredients on low until the ingredients are processed together and the walnuts turn into a flour consistency.
Continue to process the mixture while drizzling 2 teaspoons of maple syrup into the food processor. Only process with the maple until combined, do not let the mixture turn into a dough. Set the walnut mixture aside.
Place the thin apple slices into a large bowl and toss the apples with 1 tablespoon of lemon juice. Sprinkle 1 teaspoon brown sugar, ½ teaspoon of cinnamon, and ¼ teaspoon salt over the apples and toss the ingredients together.
Remove the pie crust from the fridge and pour the walnut mixture into the middle of the pie crust. Spread the walnut mixture over the pie crust, but leave 1.5-inches of pie crust clean at the edges.
Next, begin layering the apples on top of the walnut mixture. Start in the middle of the pie crust and overlap the apples in layers moving towards the edge of the pie crust. Only place the apples on the pecan mixture. Stop when you reach the clean edges of the pie crust.
Fold the pie crust over the apples to create a beautiful crust. Set aside.
Now, brown the butter. Place the butter in a small saucepan. Turn the heat to medium/high to fully melt the butter. When the butter begins to caramelize, turn the heat off and let sit in the pan until all butter has browned.
Brush the butter mixture over the pie crust and the apples with a pastry brush.
Place the galette into the oven and bake for 15 minutes. Turn the pan around in the oven and bake for an additional 15 minutes or until the pie crust begins to brown.
Remove the galette from the oven and let it rest for 10 minutes.