1. Preheat oven to 400°.
2. Combine first 3 ingredients in a medium saucepan over medium-low heat; cook 3 minutes or until berries begin to pop, stirring frequently. Set aside.
3. Weigh or lightly spoon flour into dry measuring cups; level with a knife. 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. Place mixture in a large bowl; add milk, stirring just until moist. Turn mixture out onto a lightly floured surface. Press mixture into a 7-inch circle; cut into 8 wedges. Place wedges 1 inch apart on a baking sheet. Combine egg white and 1 tablespoon water in a small bowl. Lightly brush tops of wedges with egg white mixture; sprinkle evenly with turbinado sugar. Bake at 400° for 20 minutes or until golden brown. Cool on a wire rack.
4. Place cream in a medium bowl; beat with a mixer at medium speed until soft peaks form. Add powdered sugar, beating until stiff peaks form. Split shortcakes in half horizontally; spoon 1/3 cup berry mixture over each bottom half. Top each with 1 1/2 tablespoons whipped cream; cover with shortcake tops.