First make dough by combining dry ingredients in a large bowl. Cut the cold butter into cubes and use a fork or your fingers to mix it into the dry ingredients until it resembles coarse crumbles. Add the cold water and vinegar and knead for 5-10 minutes until it comes together into a dough (can add a bit more water if needed but it will not need much more). Wrap dough in saran wrap and store in the fridge until filling is ready.
For filling, half, core, and thinly slice each apple and place in a bowl with all other ingredients. Let sit for 5 minutes, drain any collected liquid, and saute the apples for about 5 minutes on medium-high heat or until starting to turn golden.
Preheat oven to 425 degrees. Remove dough from fridge and roll out into a circle. Transfer this onto a parchment paper-lined baking sheet and sprinkle over some extra sugar. Add the apple filling in the center and fold the crust over, pinching and pulling over.
Cook in oven for 20 minutes. Meanwhile, make caramel sauce by heating all ingredients in a pot on medium-high heat until starts to turn golden, and then set aside. After 20 minutes, remove galette and spoon over some caramel sauce. Place back in oven for 5-10 minutes or until the crust starts to turn golden.
Serve warm and optionally with vanilla ice cream.