Chop butter into cubes and place in the fridge while you assemble the rest of the ingredients. Fill a small bowl with some cold water and an ice cube. Stir the ice cube around a bit and set bowl aside.
In a food processor, pulse to combine the flour, baking powder, sugar, and salt. Add the cubed butter and pulse until the dough forms pea sized balls. Add the cold water a tablespoon at a time while continuing to pulse mixture until mixture just starts to come together. Be careful not to add too much water.
Turn dough out onto a sheet of plastic wrap. Pat and press dough together to make one piece. Shape and flatten dough into a disk, wrap it with the plastic wrap. Refrigerate for 1 hour.
While the dough is almost finished chilling, prepare the filling. In a medium sized bowl, mix together the berries, sugar, cornstarch, ginger, mint and salt. Place filling in refrigerator for about 10 minutes while you roll out the pie crust.
Preheat oven to 400 F. Place dough between two sheets of parchment paper. Roll dough out into a 12 inch circle. The edges can be left ragged, no need to trim them since galettes are typically rustic looking. Place parchment paper with dough on it onto a baking sheet.
Place filling in a strainer to strain any juices or use a slotted spoon to spoon the fruit (minus the juices) onto the dough. Leave a 1 1/2 inch border. Spread the fruit out into one even layer rather than a big heaping pile. Fold edges and gently press down to seal the dough.
Beat the egg and water in a small bowl. Brush the edges with the egg wash and generously sprinkle with coarse sugar. Bake 33-37 minutes until crust is golden brown and the filling is bubbling in the middle. Allow to cool at least 10 minutes before slicing.