Heat the butter in a skillet over medium heat until it melts. Reduce the heat to medium-low and swirl it in the pan as you wait for it to become a golden brown color. Keep an eye that the milk solids at the bottom of the pan do not turn black, as this will lead to a bitter flavor. Pour the browned butter into a bowl to cool down.
While the butter is cooling, sift together the flour, almond flour, and powdered sugar. Make a well in the middle of the dry ingredients and pour in the egg whites and vanilla extract. Stir everything together until the dry ingredients are incorporated.
Pour in the cooled, browned butter and stir until it is all incorporated and the batter is silky and smooth.
Gently fold in the raspberries and pour the batter into a greased 8 inch (20 cm) cake pan. Bake in a 375℉ / 190℃ pre-heated oven for 35-40 minutes or until a toothpick inserted into the cake comes out clean.
Let cool in the pan and then serve at room temperature with a sprinkle of powdered sugar and a dollop of whipped cream.