Preheat oven to 350º. Butter and flour or line with lightly sprayed parchment paper, a 8"-9"springform or cake pan.
Combine the eggs and sugar in the bowl of an electric mixer. Beat at medium high speed for 5 minutes or until pale and lemon yellow in color. They should be slightly thickened. Gradually add the flour, milk and butter, stopping to scrape down the sides of the bowl after each addition. Beat at low speed until each ingredient is blended and then increase speed to medium high and beat for 3 minutes. Add the baking powder and vanilla and beat an additional 2 minutes to blend.
Scrape batter into prepared pan. Arrange apple slices vertically, with the core side down, in concentric circles in the batter, beginning with the outside edge of the pan and continuing to the center. The arrangement of apples should resemble a rose in full bloom.
Bake for about 50 minutes or until a toothpick inserted in the center of the cake comes out clean and apples are lightly browned. Let cool for about 10 minutes and then, if using a springform pan, remove the sides. If using a cake pan, invert onto a cardboard, remove the parchment paper and flip over onto a serving platter to reveal the apple slices. Dust cake with powdered sugar.