To make the topping, butter a 9-inch round cake pan. Put the butter and brown sugar in the prepared pan and place the pan over medium heat. Heat, stirring occasionally, until the butter is melted and the sugar has dissolved. Scatter the cranberries over the butter-sugar mixture. Set aside.
Preheat an oven to 350°F.
To make the cake, in a bowl, mix together the flour, baking powder and salt. In another bowl, using an electric mixer, beat the butter and granulated sugar on medium-high speed until light and fluffy, 2 to 3 minutes. Add the egg yolks one at a time, beating well after each addition. Add the vanilla and mix well. Using a silicone or rubber spatula, fold in the flour mixture in three additions, alternating with the milk.
In a bowl, using a whisk or an electric mixer, beat the egg whites until soft peaks form. Add the cream of tartar and continue to beat until stiff peaks form. Using the spatula, fold the whites into the batter.
Spoon the batter over the cranberries in the cake pan, spreading it evenly. Bake at 350 for 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 the pan.