1) Preheat oven to 400°F. Line baking sheet with parchment paper.
2) Whisk dry ingredients for biscuits (flour, 6 tablespoons sugar, salt, and baking powder) in large bowl.
3) Add butter; rub in with fingertips until very coarse meal forms (oatmeal-size flakes). Mix in 1/4 cup chopped ginger. Add ginger ale and 2 tablespoons cream. Toss until moist clumps form.
4) Roll dough out carefully into rectangle about 3/4 inch thick. Cut into 6 squares to make biscuits.
5) Move biscuits to baking sheet and brush with cream and sugar mixture.
6) Bake at 400 degrees for 18-20 minutes. Cool on sheet.
7) For peaches, toss peaches in large bowl with 4 tablespoons sugar and 2 tablespoons chopped ginger. Whisk remaining 1 1/4 cups cream and 2 tablespoons sugar in medium bowl to peaks.
8) Halve shortcakes horizontally. Place bottoms on plates. Top each with peaches, whipped cream, and shortcake top.