Serve this dessert in the height of summer, when peaches are fresh and juicy.
Heat oven to 400 degrees. Slice peaches; sprinkle with kirsch or schnapps, if desired, and 1 tablespoon granulated sugar. Set aside.
In the bowl of a food processor, combine the rest of the dry ingredients. Add butter; process with on-off pulses until mixture resembles coarse meal. While pulsing, slowly add enough cream or milk until dough just comes together.
Turn out dough onto a lightly floured board, and knead once or twice. Pat into a 3/4-inch-thick square. Trim edges, and cut into four squares. Brush with additional cream or milk; sprinkle with sugar.
Place on a lightly buttered baking sheet; bake for 20 to 25 minutes. Transfer cakes to a wire rack, and allow to cool slightly.
Meanwhile, whip the cream: In a large bowl, beat the heavy cream and vanilla extract until stiff peaks form; set aside. Split cakes horizontally. Place bottom halves on dessert plates, and top with peaches and vanilla whipped cream. Cover with top halves of shortcakes, and serve.
Blanch the peaches in boiling water to remove the skins, if you like.