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.
Beat butter and 2/3 cup sugar with an electric mixer at medium-high speed until pale and fluffy, about 2 minutes, then beat in vanilla. Add egg and beat well.
At low speed, mix in flour mixture in 3 batches, alternating with buttermilk, beginning and ending with flour, and mixing until just combined.
Spoon batter into cake pan, smoothing top. Scatter raspberries 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, 25 to 30 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.