Preheat the oven to 375.Grease a 9x13 pan with butter. (Can line with buttered parchment if you prefer).Stir the sugar, baking powder, flour, salt, and zest in a bowl. Cut in the butter and egg using a pastry blender or a fork or two butter knives. It will be crumbly. Divide it in half. Press half the mixture in the bottom of the pan. Bake it for 10 minutes.Gently stir the mulberries with 1/3 cup sugar, juice, and cornstarch.Spread the berry mixture over the warm crust, then crumble the remaining dough over the top.Bake for about 30 minutes, or until the top crust begins to brown. Cool completely. Slices best after refrigerating.