Preheat oven to 400° F. and place rack in centre of oven. Grease a 9 or 10-inch cake pan and line the bottom with parchment paper, for easy removal. (You can also bake this in a greased 10-inch top diameter cast-iron skillet, if you like).
In a small bowl, whisk together the flour, baking powder, baking soda and salt. Set aside.
With an electric mixer or with a stand mixer fitted with the paddle attachment, beat the butter and sugar at medium-high speed until light and fluffy, about 2 minutes. Beat in the vanilla. Add the egg and beat well.
With the mixer at low speed, add the flour mixture in 3 batches, starting with 1/3 of the flour, then 1/2 of the buttermilk, then half the remaining flour, the rest of the buttermilk and finishing with the remaining flour mixture. Mix just until combined.
Spoon the batter into prepared cake pan or skillet, smoothing top. Scatter raspberries evenly over the top and sprinkle with remaining 1 1/2 tablespoons sugar.
Bake until cake is golden and a wooden pick inserted into centre comes out clean, about 25 to 30 minutes. Cool in the pan 10 minutes. If baked in a skillet, serve right from the skillet. If baked in a cake pan, then turn out onto a rack and allow to cool 10 to 15 minutes more. Invert onto a plate.
*Make your own buttermilk substitute by combining 1/2 cup regular milk with 1 1/2 tsp of lemon juice or white vinegar. Let stand for 10 minutes then use in place of the buttermilk in this recipe.Be sure to read the Ingredient and Baker's Tips above this Recipe Card, where I share some valuable tips, options, substitutions and variations for this recipe!