Preheat oven to 350 degrees. Lightly butter a 10″ round baking pan (a 9×12 pan works, too).
Sprinkle the brown sugar in the bottom of the pan. Pour 6 Tbsp. of the melted butter evenly over the brown sugar, then lay the berries evenly on top.
Using an electric mixer on medium-high speed, beat together the 1/2 cup of butter and the granulated sugar until creamy. Add the eggs, one at a time, beating well.
Fold in the flour, baking powder, baking soda and salt into the butter mixture. Stir in the cream and vanilla until smooth.
Spoon the batter evenly over the raspberries.
Bake until the top is golden and a toothpick inserted into the center of the cake comes out clean, about 35 minutes. Remove from the oven; transfer the cake to a wire rack and cool for 10 minutes.
Run a knife blade around the edge of each cake to loosen it from the ramekin. Invert the cake onto a serving plate. Lightly tap the bottom of the pan to loosen the cake, then lift the pan.
Serve the cake warm and top with whipped cream if desired.