Combine the flour, sugar, and salt in a bowl. Add the cubed butter and toss to coat. Dump the mixture out onto a clean surface and use a rolling pin to roll the butter into thin sheets, combining it with the flour. Use a bench scraper to scrape the rolling pin and to bring the mixture back into a pile as necessary. Continue until all of the butter is incorporated into the flour.

Add the buttermilk. Use a spoon and then your hands to stir the mixture until it comes together into a ball. If mixture is too dry, add the water or vodka a tablespoon at a time. Divide the dough into 8 equal portions and flatten into disks. Wrap each disk in plastic wrap and chill in the fridge for at least 1 hour.

On a lightly floured surface, use a rolling pin to roll out each disk of dough into a rough 6 inch circle.

Combine the sugar, water, and chopped ginger in a small saucepan over medium high heat, stirring to dissolve the sugar. Bring to a boil, then reduce heat and simmer for 5 minutes. Remove from heat and cover pan and let sit until cooled to room temperature. Store in the fridge until ready to use.

Toss the chopped pineapple and mango with the sugar, cornstarch, and ground ginger. Divide equally among the dough rounds, leaving one inch space around the edges. Fold edges of the dough up over the fruit.

Let cool to room temperature, then brush with simple syrup. Store leftover galettes in the fridge.