Cut the butter into 1/2 inch cubes. Keep the cubed butter and buttermilk in the fridge until ready to use.
In a bowl, whisk together the flour, sugar, and salt.
Add the cubed butter to the flour mixture and toss to coat. Using your thumbs against your index fingers, press the butter cubes into planks. Toss them with the flour as you work. Stop once you've pressed all of the butter and have a mixture of pea size to walnut-half size butter pieces.
Add the buttermilk and mix. If the dough clumps easily, you have enough liquid. If not, add a teaspoon more buttermilk until the dough does clump easily.
Dump the dough out onto a lightly floured surface and knead gently by folding it over itself 2 to 3 times.
Shape the dough into a disk and wrap it in a towel. Chill the dough while you prepare the apples.
Apple Filling
In a bowl, whisk together the sugar, flour, and cinnamon.
Peel, core, and dice the apples into 1/2 inch cubes.
Add the diced apples and vanilla extract to the cinnamon sugar mixture and toss to coat. Set aside.
Assembling the Galettes
Line a baking sheet with parchment paper.
Remove the dough from the fridge and place it on a lightly floured work surface.
Using a lightly floured rolling pin, start in the center and roll out. Rotate and roll from the center out. Continue this until the dough is about 1/8th inch thick and about 12 inches across. (see notes #1 and #2)
Cut 4-inch rounds out of the dough. Press the scraps together and roll back out to get another 4 rounds. (see note #3)
Spoon 1 tablespoon of apples onto the center of one of the dough rounds leaving space around the edges.
Fold up the edges and pleat as you go, pressing down to secure them. Transfer the mini galette to the parchment-lined baking sheet and continue with the rest of the galettes.
Freeze the galettes for 1 hour. (see notes #4 and #5)
Baking the Galettes
Preheat the oven to 375 degrees F.
Transfer the frozen galettes and parchment paper to a new baking sheet. (see note #6)
Brush one galette with the melted butter then immediately sprinkle with sugar. Continue with the rest of the galettes.
Bake for 40 to 50 minutes, or until the crust is golden brown and the apples are softened.
Serve warm with vanilla ice cream.
Notes
If the dough begins to stick, add a bit more flour to the work surface and/or rolling pin.
If the dough begins to feel warm or the butter gets too soft, transfer the dough to a baking sheet and chill in the fridge for 10 minutes before continuing.
You'll probably have more dough scraps but rolling out a third time can lead to tough dough. Either discard the leftovers or cut them into decorative shapes to place on top of the galettes.
Freezing the galettes before baking them helps them keep their shape and increases the flakiness of the crust.
At this point, you can transfer the frozen galettes to a freezer bag and keep them in the freezer for up to 3 months.
This is important because placing the frozen baking sheet into a hot oven can cause it to warp.