Preheat the oven to 350°. Set a 9-inch nonstick cake pan over moderate heat. Add 4 tablespoons of the butter and when it is melted, stir in the brown sugar until dissolved, about 1 minute. Remove from the heat. Arrange the lemon slices in the melted brown sugar.
In a medium bowl, whisk the flour with the baking powder and salt. In a large bowl, with an electric mixer, beat the remaining 8 tablespoons of butter with the granulated sugar until light and fluffy. Beat in the vanilla and the egg yolks, one at a time. At low speed, beat in the dry ingredients in 3 batches, alternating with the milk.
In a stainless steel bowl, beat the egg whites with the cream of tartar at high speed until firm peaks form. Fold one-third of the beaten whites into the batter, then fold in the rest. Scrape the batter into the prepared pan and bake for about 30 minutes, or until a toothpick inserted in the center of the cake comes out clean. Let cool in the pan for 15 minutes, then invert it onto a plate. Serve warm or at room temperature with whipped cream.