Preheat oven to 375°.
Combine blackberries and apple. Combine 1 cup sugar, 2 tablespoons flour, and lemon rind; toss with fruit. Stir in vanilla; set aside.
Combine 3/4 cup flour, 2 tablespoons sugar, baking powder, and salt in a large bowl. Cut in 3 tablespoons cold butter with a pastry blender or 2 knives until mixture resembles coarse meal. Add egg white; sprinkle ice water, 1 teaspoon at a time, over surface until mixture forms a loose ball. (Dough will be slightly crumbly.) Place mixture on heavy-duty plastic wrap; pat dough 3 or 4 times to form a disc. Cover with additional plastic wrap. Roll dough, still covered, into an 8-inch square. Chill 10 minutes.
Toss fruit mixture gently; spoon into an 8-inch square pan coated with cooking spray. Dot with 2 tablespoons butter.
Remove 1 sheet of plastic wrap from dough; invert dough over fruit mixture in pan. Remove top sheet of plastic wrap.
Combine 1 1/2 teaspoons sugar and cinnamon; sprinkle over crust. Bake at 375° for 35 minutes or until crust is browned. Let stand 15 minutes before serving.