Preheat the oven to 400* F. Roll out the pie dough until it's 1/8 inch thick. Place in the fridge while you prepare the remaining ingredients.
In a medium bowl, toss the apple slices with the lemon juice. Add the sugar, flour, cinnamon, cardamom, allspice, and salt. Toss to combine. Place the apple filling in the center of the pie dough, leaving a two inch rim on all sides. Fold the rim over the apples, ensuring the filling stays inside.
Whisk together the egg with 1 Tablespoon of water. Brush the crust with the egg wash, and sprinkle with demerara sugar. Bake for 45-60 minutes.
While the galette is baking, combine the butter, dark brown sugar, cream, and salt in a small saucepan. Heat over medium-high, stirring constantly. Bring to a boil, and let it cook for two or three minutes. Remove from heat, and add the vanilla and brandy. It will bubble up, just keep stirring! Let it cool slightly, and store it in a jar. Refrigerate until use (you may have to heat it up before serving).
Serve the apple galette warm with ice cream or whipped cream and the butterscotch sauce.