In a medium mixing bowl, whisk together the flour, salt, and sugar for the pie crust. Grate in 1/3 cup of frozen butter, and toss to coat. Sprinkle in 5 to 7 tablespoons of ice cold bourbon (bourbon that has been poured over ice and let to sit until it's chilled).
Mix with your hand, squeezing to test for hydration. It should easily form together like clay. Dump the contents onto your work surface and form the dough into a ball. There should be few dry patches, but it should all come together as a whole.
Flatten your dough into a 1-inch thick disk, wrap, and place in the fridge for 1 hour.
Caramel Sauce
In a small saucepan, bring sugar and water to a boil. Brush the sides of the pot down with a damp pastry brush to avoid crystals.
When the mixture is amber-colored, or 350ºF on a candy thermometer (this will take between 6 and 12 minutes depending on your stove), remove from heat. Whisk in cubes of butter until combined.
Continue whisking as you slowly drizzle in the milk, vanilla, bourbon, and salt. Cool completely before use.
Prep the Apples
Peel, core, and slice your apples into 1/4 inch thick half-moon slices and place in a mixing bowl. Toss with cinnamon and ginger, and cover until the caramel is cooled, and the pie dough is chilled.
Constructing the Galette
Preheat the oven to 400ºF.
Flour your work surface and roll out the pie dough to a little less than 1/4 inch thick, and 16 inches diameter.
Place a sheet of parchment on your baking sheet, and transfer the pie dough to the parchment paper.
Spread 1/2 cup of caramel sauce in the center of your crust and spread it into a 12-inch diameter circle.
Place the apples in whatever design you wish over the caramel, and top with an additional 1/4 cup of caramel sauce.
Fold the sides of your pie dough up and over the apple filling, leaving the center exposed.
Brush the top of the pie dough with egg whites and sprinkle with turbinado sugar.
Bake for 30 to 35 minutes.
Cool on the baking sheet for 10 minutes, and then transfer to a cooling rack to cool the rest of the way. To serve, top with vanilla ice cream and more caramel sauce.