Preheat the oven to 350°F.
Grease a 10-inch round springform pan with oil and line the bottom with a round of parchment paper.
To prepare the cake: In the bowl of a standing mixer fitted with the paddle attachment, combine the butter and granulated sugar until creamy. Add the yolks, one at a time, and beat until incorporated, then add the vanilla. Sift in the flour and baking powder and stir until combined. Spread the batter into the prepared pan. It may seem like there isn’t enough to go around, but use wet hands to spread the batter over the bottom of the pan. Arrange the plums, skin side down, over the batter, leaving a 1-inch space between the edge and the plums.
To prepare the topping: In the bowl of a standing mixer fitted with a paddle attachment, combine the butter and brown sugar and beat until soft. Add the flour, rolled oats, and star anise powder. Using your finger- tips, rub the butter mixture into the dry ingredients until the mixture begins to clump together. Sprinkle the topping over the top of the cake. Place the whole star anise in the center of the cake, pushing down slightly to secure it in the crumb topping. Bake the cake for about 50 minutes, until golden brown. Let cool completely.
Unmold the cake, peel away the parchment paper, and place on a serving plate. Tap some confectioners’ sugar through a sieve onto the top of the cake for decoration.
Source: The Modern Menu Cookbook
Photos by Andrew Zuckerman