Preheat oven to 400°F with rack in middle. Butter and flour a 9-inch round cake pan.
Whisk together flour, baking powder, baking soda, and salt and set aside. In a larger bowl, beat butter and 2/3 cup sugar with an electric mixer at medium-high speed until pale and well mixed, then beat in vanilla and zest, if using. Add egg and beat well.
At low speed, mix in flour mixture in three batches, alternating with buttermilk, beginning and ending with flour, and mixing until just combined.Spoon batter into cake pan, smoothing top. Arrange blackberries evenly over top and sprinkle with remaining 1 1/2 tablespoons sugar.
Bake until cake is golden and a wooden pick inserted into center comes out clean, 20 to 25 minutes. Cool in pan 10 minutes, then turn out onto a rack and cool to warm, 10 to 15 minutes more. Invert onto a plate.