Set an oven rack in the center and heat the oven to 400°F. Put parchment paper on one baking sheet and set it aside.
Mix butter with the dry ingredients. There are two methods to accomplish this: in a big bowl or inside the food processor. Place flour, brown sugar, granulated sugar, baking powder, salt, and cubed butter in the food processor's body. Until the butter is completely mixed into the flour mixture, pulse the mixture. Next, transfer this mixture into a large basin. Alternatively, place flour, brown sugar, granulated sugar, baking powder, and salt in a large mixing basin and whisk to incorporate well. Toss to coat after adding the butter to the bowl. Next, either spread the butter into the flour with your hands or chop it into the flour with a pastry blender. Keep doing this till you see shaggy flecks throughout the flour.
Add peaches and wet ingredients together. Whisk the egg, almond extract, vanilla bean paste or extract, and buttermilk together in a separate basin until well combined. Pour the buttermilk mixture and cut peaches into the flour mixture. Take care not to overwork the scone dough as you gently mix it together until you have a combined mass. If the dough is too sticky, add another tablespoon of flour and mix it in until it's just blended. The dough should feel slightly sticky.
Move to the surface of work. After lightly flouring your work area, remove the dough from the bowl and place it there. Gently form and pat the dough into an 8-by-8-inch circular disk approximately 1 inch thick using your lightly floured hands.
Press and form the scones. As shown in the photo, divide the dough into 8 equal triangle-shaped wedges using a sharp knife or bench scraper.
Chill the scones. To allow the scones to rise and puff up, place the formed scones on the prepared baking sheet, spacing them about an inch apart. While the oven is still heating up, put them in the refrigerator to cool for at least half an hour. <> Remember not to omit the chilling phase. The butter will have softened after working with the dough; the chilling period makes sure that it solidifies once more and gives the scones time to firm up.
Apply and bake. Remove scones from the refrigerator. Lightly brush each scone's top with a little buttermilk (or heavy cream) with a pastry brush. Next, if preferred, lightly dust each scone with demerara or Turbinado sugar. Scones should be baked for 25 to 30 minutes, turning the baking sheet halfway through, or until the tops of the scones are golden brown and have risen.
Serve with glaze. To create the frosting, mix the powdered sugar, milk, ground cardamom, and bourbon or whiskey in a small basin. Mixture should be fully mixed and lump-free after stirring. Drizzle peach scones with icing. Serve right away. Have fun!