Preheat the oven to 350°F. Spray an 8-inch square pan with cooking spray.
Lightly spoon the flour into a 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 zest, lemon juice, butter, and egg yolks, stirring with a whisk until the mixture is smooth.
Beat the egg whites with a mixer at high speed until foamy. Add 1/4 cup granulated sugar, 1 tablespoon at a time, beating until soft peaks form. Gently stir one-fourth of egg white mixture into the buttermilk mixture; gently fold in remaining egg white mixture. Fold in the blackberries.
Pour the batter into the prepared pan. Place the pan with the batter into a larger baking pan; add hot water to the larger pan to depth of 1-inch. Bake at 350°F. for 45 to 50 minutes or until the cake springs back when touched lightly in center. Sprinkle the cake with powdered sugar. Serve warm.