Preheat your oven to 400°F with the oven rack positioned in the middle.
Prepare your 9-inch round cake pan by buttering it and dusting it with flour.
In a mixing bowl, whisk together flour, baking powder, baking soda, and salt.
In another large bowl, beat the room temperature butter and 2/3 cup sugar together using an electric mixer on medium-high speed until fluffy.
Add the vanilla extract and mix it in.
Add the egg to the butter mixture and beat well until fully combined.
At low speed, gradually add the flour mixture in three batches, alternating with the buttermilk.
Spoon the batter into the prepared cake pan, smoothing the top with a spatula.
Scatter the fresh raspberries evenly over the top and sprinkle with the remaining 1-1/2 tablespoons sugar.
Bake until golden brown and a wooden pick inserted into the center comes out clean.
Cool in the pan for about 10 minutes before turning out onto a rack.
