Preheat oven to 400°F.
Line bottom of a buttered 8- by 2-inch round cake pan with 2 rounds of parchment paper, then butter parchment.
Dust pan with some flour, knocking out excess.
Arrange blackberries in 1 layer in cake pan.
Sprinkle berries with 11/2 tablespoons sugar and shake pan to help distribute sugar.
Whisk together 1 cup flour, baking soda, and salt in a bowl.
Beat together butter and remaining 1/2 cup sugar in a large bowl with an electric mixer at high speed until light and fluffy, about 2 minutes. Add egg and vanilla and mix at low speed until just incorporated. Alternately add flour mixture and buttermilk in 3 batches, mixing at low speed until just incorporated