In a medium bowl combine sliced strawberries with granulated sugar, brown sugar, and balsamic vinegar. Set aside while preparing crust.
In the bowl of a food processor, combine flour, butter, sugar, and salt. Pulse until butter is in pea sized chunks.
Add water and vodka. Pulse to combine.
Dump dough out onto a lightly floured work surface. Knead lightly to bring dough together. Refrigerate for about 30 minutes.
While dough is chilling, preheat oven to 400F.
Strain liquid from strawberries. Add pepper and cornstarch.
Remove dough from refrigerator. Separate dough into 8 equal pieces and roll each piece into a circle.
Add about 2 heaping tablespoons of strawberry filling. Using your fingers, fold the edges of the dough up partially over the filling.
Refrigerate assembled galettes for 15 minutes to set shape. Remove dough from refrigerator. Brush crust with egg wash. Sprinkle with turbinado sugar.
Bake for 25 minutes. Crust should be golden brown.
Allow galettes to cool on baking sheet.