Combine flour, 1 Tbsp. sugar, salt, ginger in food processor. Pulse to combine.
Add butter. Pulse until mixture is coarse – about 10 seconds.
While food processor is running, add 1/4 cup ice water. Test dough to see if it holds together. Add more ice water, 1 Tbsp. at a time, until it does. Dough should not be sticky or feel wet.
Place dough on parchment-lined cutting board or counter. Divide evenly into number of galettes desired and roll into circles about 1/4" thick.
Wrap circles in plastic wrap and place in fridge for 1 hour.
Preheat oven to 375°F.
While dough is chilling, mix fruit, cornstarch, and 1/4 cup sugar together in medium bowl. Let fruit rest for 30 minutes.
Remove dough from fridge and place rounds on parchment-lined baking sheet. Spoon 1/2 cup of fruit into the center of each and fold in sides. Repeat with remaining 3 galletes.
Whisk 1 egg in small bowl and brush onto crust of each gallete.
Sprinkle crust with raw sugar.
Bake for 30 minutes or until crust is golden brown.