Preheat oven to 350°. Line a 13 x 9-inch baking pan with aluminum foil; spray with nonstick baking spray with flour. Set aside.
In a large bowl, stir together 1 cup brown sugar, cornstarch, and cinnamon. Stir in peaches and bourbon, then add blackberries. Set aside.
In another large bowl, whisk together remaining 1 cup brown sugar, flour, oats, baking powder, and salt.
Using a fork or pastry blender, cut in butter until crumbly.
In a small bowl, whisk together egg, sour cream, and vanilla until smooth.
Add egg mixture to flour mixture, stirring until combined.
Press three-fourths of flour mixture into bottom of prepared pan. Stir fruit mixture; spread evenly in pan.
Sprinkle with remaining flour mixture.
Bake 45 - 55 minutes, or until bars are set and golden brown.
Cover pan with foil to prevent overbrowning during last 10 - 15 minutes of baking time if needed.
When cool, remove bars by foil handles and cut into squares.