Combine blueberries, sugar, and lime juice in a medium saucepan over medium-low heat. Cook 3 minutes or until berries begin to pop, stirring frequently. Set aside.
Place flour, baking powder, and salt in a food processor; pulse 3 times to combine. Add butter and ginger to processor; pulse until mixture resembles coarse meal.
Transfer flour mixture in a large bowl. Add milk, stirring just until moist. Turn shortcake dough out onto a lightly floured surface. Press into a 7-inch circle and using a sharp knife, cut into 8 wedges.
Place wedges 1 inch apart on a baking sheet. In a small bowl, whisk together the egg white and 1 tablespoon water. Using a silicone pastry brush, lightly brush tops of wedges with egg white mixture and sprinkle evenly with turbinado sugar.
Bake for 20 minutes or until golden brown. Cool on a wire rack.
To serve, split shortcakes in half horizontally. Spoon ⅓ cup berry mixture over each bottom half. Top with whipped topping and cover with shortcake tops.