Preheat your oven to 400F.
Peel the apples, cut them in half vertically, remove the core, and slice ¼-inch thin slices.
In a large bowl, toss the sliced apples with the ½ teaspoon cinnamon, 1 teaspoon vanilla, ¼ cup light brown sugar, 2 tablespoon granulated sugar, 2 teaspoon lemon juice, and ½ teaspoon kosher salt.
Lightly flour your surface and roll the sheet of puff pastry out with a rolling pin to fit a 10-inch cast iron with some overhang. Place it into your cast iron pan.
Add the sliced apple filling to the puff pastry-lined cast iron skillet. Then fold over the edges, brush them with the beaten egg using a pastry brush, and sprinkle them with raw sugar (the egg wash will help the sugar stick).
Bake the galette at 400F for 40 minutes until the puff pastry deeply golden brown. Serve with a scoop of ice cream.