How to Make It
Preheat oven to 400°. Beat first 3 ingredients and 2 1/4 cups flour at medium speed with a heavy-duty electric stand mixer just until combined. Place dough on a lightly floured surface; roll to 1/4-inch thickness. Cut about 14 rounds with a 2 1/2-inch fluted round cutter. Place rounds in a single layer on a baking sheet; cover and chill until ready to use.
Pulse ginger and 1/4 cup turbinado sugar in a food processor 5 to 6 times or until well combined. Stir together ginger mixture and remaining 1/2 cup turbinado sugar in a large bowl. Add lemon juice, peaches, and remaining 3 Tbsp. flour; toss to coat. Place peach halves, slightly overlapping, in a greased (with butter) 10-inch cast-iron skillet, and pour any remaining juice over peaches.
Bake at 400° for 15 minutes. Remove from oven, and nestle shortbread dough rounds among peaches. Brush rounds with egg white, and sprinkle with granulated sugar. Bake 17 to 20 minutes or until golden brown.
We tested with Sugar in the Raw Natural Cane Turbinado Sugar.