Preheat your oven to 350°F (175°C) and grease a 9-inch cake pan with butter, lining the bottom with parchment paper.

Melt 4 tablespoons of butter and 3/4 cup of brown sugar in a saucepan over medium heat, then pour into the cake pan.

Arrange the blueberries over the sugar mixture in a single layer.

Beat 3 egg whites until soft peaks form, then set aside.

Cream together 1/3 cup of softened unsalted butter and 1 cup of granulated sugar until light and fluffy; add 3 egg yolks and vanilla extract.

Whisk together 1 1/2 cups of flour, 2 teaspoons of baking powder, and 1/2 teaspoon of salt in a separate bowl; gradually add to the creamed mixture, alternating with 1/2 cup of milk.

Fold the beaten egg whites into the batter carefully.

Spoon the batter over the blueberries in the pan and smooth the top.

Bake for 55-60 minutes, testing for doneness with a toothpick.

Cool the cake in the pan for 5-10 minutes, then invert onto a serving platter.

Serve warm or at room temperature, optionally with ice cream or whipped cream.