In a medium mixing bowl, whisk together the flour, granulated sugar, salt, and cinnamon.
Use the large-hole side of a box grater to grate in the cold butter. Use hands to gently toss the butter into the flour mixture until it’s dispersed, with no large clumps remaining.
Sprinkle the vanilla extract over the flour mixture. Add 3 ½ ounces of ice water and fold in partially with a spatula. Use hands to finish bringing dough together, adding the remaining ½ ounce water if needed. The dough should be slightly tacky, but not overly sticky or dry.
Press dough into a round disc, wrap in plastic wrap, and refrigerate for one hour.
In a small bowl, whisk together brown sugar, corn starch, cinnamon, nutmeg, and all spice for filling.
Flour a large sheet of parchment paper to use as a rolling surface. Roll chilled dough out to a 12” circle, dusting dough with flour as needed to prevent sticking. If desired, use a knife to trim any uneven edges.
Leaving a 1 ½” clear border around the outer edges, arrange apple slices concentrically over the galette dough, working from the outside towards the center. The apple slices should partially overlap. Sprinkle filling mixture evenly over the fruit when done.
Use parchment to carefully lift the outer edges of the galette and fold them over the border of the fruit filling, forming a crust. If dough cracks, use your fingers to gently patch it back together.
Slide parchment onto a baking sheet and place assembled galette in freezer for 10 minutes. Meanwhile, preheat oven to 400ºF.
Just before baking, brush galette crust with melted butter, pouring any remaining butter directly over the fruit filling. Sprinkle galette liberally with raw sugar.
Bake galette in preheated oven for 30-40 minutes, or until the crust is golden. Serve warm, optionally with whipped cream or ice cream.