Lightly spoon the flour into a dry measuring cup, and level with a knife. Combine the flour, 2/3 cup granulated sugar, salt, and nutmeg in a large bowl; add the buttermilk, lemon rind, lemon juice, butter, and egg yolks, stirring with a whisk until the mixture is smooth.
Beat egg whites with a mixer at high speed until foamy. Add 1/4 cup granulated sugar, 1 tablespoon at a time, beating until stiff peaks form. Gently stir one-fourth of egg white mixture into the buttermilk mixture; gently fold in remaining egg white mixture. Fold in blackberries.
Pour the batter into an 8-inch square baking pan coated with cooking spray. Place in a larger baking pan; add hot water to larger pan to depth of 1 inch. Bake at 350° for 35 minutes or until the cake springs back when touched lightly in center. Sprinkle cake with powdered sugar. Serve warm.