Cut a round piece of parchment paper to fit the bottom of a 9-inch round cake pan. Spray the pan with flour baking spray, place the cut parchment round in the pan, then spray again.
In a medium bowl, whisk together the flour, baking powder, baking soda, and salt. Set aside.
In another medium bowl, beat together the butter and 2/3 cup sugar with an electric mixer on medium-high. Beat until light and fluffy, about 3 minutes. Then beat in the vanilla. Next add the egg and beat until incorporated.
At low speed, combine the flour mixture with the butter mixture in 3 batches, alternating with the buttermilk. Begin and end with the flour and mix until just combined.
Pour the batter into the prepared cake pan and smooth the top with a spatula. Scatter the raspberries over top of the batter, then sprinkle with the remaining 1 1/2 tablespoons of sugar.
Bake 25-30 minutes or until the cake is golden and a toothpick inserted near the center comes out clean.
Cool the cake in the pan for 10 minutes. Then, invert the cake to remove it from the pan. After removing the parchment paper, place the cake right side up on a wire rack. Allow the cake to cool 10-15 more minutes. Serve warm.