To prepare berries, combine first 5 ingredients; toss to combine. Cover and chill 1 hour.
Preheat oven to 375°.
To prepare cake, place a rack in the lower third of oven. Lightly spoon flour into a dry measuring cup; level with a knife. Sift together flour, 1/2 cup powdered sugar, and ginger in a medium bowl. Sift together remaining 1/2 cup powdered sugar and 3/4 cup granulated sugar in another bowl. Place egg whites in a large bowl; beat with a mixer at high speed until foamy. Add cream of tartar and salt; beat until soft peaks form. Add powdered and granulated sugar mixture, 1 tablespoon at a time, beating until stiff peaks form. Sift flour mixture over egg white mixture, 1/4 cup at a time; fold in. Fold in 2 tablespoons juice.
Spoon batter into an ungreased 10-inch tube pan, spreading evenly. Break air pockets by cutting through batter with a knife. Bake at 375° for 30 minutes or until cake springs back when lightly touched. Invert pan; cool completely. Loosen cake from sides of pan using a narrow metal spatula. Invert the cake onto a plate.
Cut 1 inch off top of cake using a serrated knife; set top of cake aside. Hollow out bottom of cake using a small knife, leaving a 1-inch-thick shell; reserve torn cake for another use.
To prepare whipped cream, place cream in a medium bowl; beat with a mixer at high speed until soft peaks form. Scrape seeds from vanilla bean into bowl; discard pod. Gradually add 3/4 cup powdered sugar, beating at high speed until stiff peaks form.
Spoon all but 1 cup of berry mixture into cake shell; top with whipped cream. Replace top of cake; sprinkle with 2 tablespoons powdered sugar. Serve immediately with additional berry mixture; garnish with orange rind, if desired.
For perfect whipped cream, use a bowl that's large enough to allow the cream to double in volume. Refrigerate the bowl and beaters for at least half an hour, or place them in the freezer for 15 minutes, and make sure the cream is very cold. Use the freshest whipping cream available, and add sugar, vanilla, or any other ingredients near the end of whipping; adding them too soon in the process will decrease the amount of volume.