For the dough: In the bowl of a stand mixer, whisk the 2 1/2 cups flour, 1/2 cup granulated sugar and salt together on low speed. Change to the paddle attachment. Add the butter and beat until the mixture appears crumbly. Add the egg and beat until the dough clings to the paddle. *This dough can made with a stand mixer or food processor
Transfer the dough to a clean work surface. Divide into 2 balls. Place one of the dough balls onto a sheet of parchment paper and top with another sheet. Roll the dough until it is 1/8 inch thick. Roll out the other piece of dough the same way. Refrigerate until firm, about 1 hour.
Preheat the oven to 375˚ with the oven racks in the upper and lower thirds of the oven.
In a small bowl combine the brown sugar, ginger, blueberries, vanilla and remaining 1 tbsp flour.
Line two baking sheets with parchment paper. Remove one dough sheet from the fridge. Cut as many 3 inch cookies as you can from the dough and place on the parchment lined baking sheet two inches apart. Knead the leftover pieces and roll into another 1/8 inch sheet. Place the remaining dough back in the fridge. Repeat the cookie cutting with the other refrigerated piece of dough. Continue to cut cookies until you have used up all the dough, transferring it in and out of the fridge as it gets too soft to work with.
Place a small amount of blueberry filling (about 1 tbsp) into the middle of half of the cookies. Place the tops on the cookies, press to seal the edges with a fork. Poke some holes on the tops to let steam escape. Brush with egg wash and sprinkle with the Turbinado sugar.
Bake for 22-25 minuets, rotating sheet pans half way through baking time.
When the cookies are golden brown, remove from the oven and cool on cooling racks.