Preheat the oven to 425°. Line a baking sheet with parchment or a silpat baking mat.
In a food processor fitted with a metal blade, combine the flour, baking powder, and salt. Add the butter cubes and pulse until coarse crumbs are formed. (If you don’t have a food processor, simply cut in the butter with a pastry blender or two knives.)
Transfer the crumb mixture to a mixing bowl. Stir in the half and half to form a stiff dough.
On a lightly floured surface, turn out the dough and pat it into an 8 inch circle. Cut the round into 8 wedges. Sprinkle the dough with the demerara sugar.
Transfer the wedges to the prepared baking sheet, spacing them apart. Bake for 20 minutes or until golden. Cool on a rack.
Meanwhile, combine the sliced peaches, granulated sugar, and lime juice in a medium sized mixing bowl. Allow to set about five minutes.
To serve: Slice a shortcake wedge in half horizontally. Top the bottom half with peach slices and a scoop of ice cream. Place the top of the shortcake over the ice cream and serve immediately.
The shortcakes can be made up to 2 days in advance. Store in an airtight container at room temperature. For longer storage, place in the freezer.Nutritional values are approximate and based on 1 shortcake with peaches and ice cream.