Preheat the oven to 375°F (190°C).
Butter a 9×13 inch pan, or spray it with a nonstick spray.
In a medium bowl, stir together sugar, baking powder, flour, salt and spices with a whisk. Use a pastry blender, fork or your fingertips, blend the butter and egg into the flour mixture. It will be crumbly. Pat 3/4 of the crumbs into the bottom of the prepared pan, pressing firmly.
Cut peaches into thin slices and add to a bowl of 2 Tablespoons brown sugar, a squeeze of lemon juice, and a light sprinkle of cinnamon. Stir gently and let stand for 5 minutes.
Arrange peach slices over crumb base in a single layer. Add blackberries. Scatter remaining crumbs evenly over fruit and bake in preheated oven for 30 minutes, until top is slightly brown and you can see a little color around the edges.
Cool completely in pan before cutting into squares.