Preheat the oven to 350 degrees F (175 degrees C). Butter a 9-inch round cake pan.

Place brown sugar and butter into the prepared pan and place the pan over medium heat. Heat, stirring occasionally, until butter is melted and sugar has dissolved, 3 to 5 minutes. Scatter cranberries over the butter-sugar mixture. Set aside.

Mix flour, baking powder, and salt together in a bowl.

Beat white sugar and butter together in another bowl using an electric mixer on medium-high speed until light and fluffy, 2 to 3 minutes. Add egg yolks, 1 at a time, beating well after each addition. Add vanilla extract and mix well. Fold in the flour mixture in 3 additions using a silicone or rubber spatula, alternating with milk.

Beat egg whites in another bowl using a whisk or an electric mixer until soft peaks form. Add cream of tartar and continue to beat until stiff peaks form. Fold whites into the batter using a spatula. Spoon batter over the cranberries in the cake pan, spreading evenly.

Bake in the preheated oven until a toothpick or skewer inserted into the center of the cake comes out clean, 55 to 60 minutes. Transfer the pan to a wire rack and let cool for 15 minutes. Run a knife around the edges of the pan to loosen the cake. Invert onto a serving plate, let stand for 5 minutes, then lift off pan.

Whip heavy cream in a bowl using a whisk or an electric mixer until soft peaks form. Stir in confectioners' sugar and vanilla extract.

Cut the cooled cake into wedges and top with whipped cream.