Preheat the oven to 375 degrees. Line a 9×13 inch baking dish with aluminum foil. Spray the foil with cooking spray or lightly grease with butter. In a large bowl combine lemon zest and 1 cup of sugar. Rub the zest into the sugar using a spoon or fork until it becomes somewhat moist. Add flour, baking powder, and salt. Use a fork to blend in the butter. Stir in the egg. The dough should be crumbly and wet.
Pat half of the dough evenly onto the bottom of the prepared baking dish. In a separate bowl stir together 1/8 cup of sugar and 3 teaspoons of cornstarch. Gently stir in the blackberries and blackberry jam. Spread the blackberry mixture evenly over the crust. Crumble the remaining dough over the blackberry layer.
Place into the oven and bake at 375 degrees for 45 minutes or until the top is slightly browned. Allow the bars to cool completely before cutting into squares.
In a large bowl, beat the cream cheese until smooth. Sift in the powdered sugar. Add the milk, a little at a time, until the glaze has reached a consistency that it can be drizzled over the bars using a fork. Drizzle the frosting over the cooled brownies.