Preheat the oven to 350 degrees F (175 degrees C). Grease a large Kugelhopf or Bundt® cake pan with butter.
Beat butter with an electric mixer in a large bowl until light and creamy. Slowly add sugar and vanilla sugar while beating constantly. Add eggs, 1 at a time, beating well after each addition. Beat for 5 minutes until batter is light and fluffy.
Sift flour and baking powder together in a separate bowl. Gradually mix flour mixture into the cake batter, alternating with the milk. Add rum and lemon zest. Pour 2/3 of the batter into the prepared pan.
Stir cocoa powder into the remaining batter until fully incorporated. Pour chocolate batter over the vanilla batter in the pan. Gently move a knife up and down through the batter in circular movements to create a marbled effect.
Bake cake in the preheated oven until a toothpick inserted in the center comes out clean, 50 to 60 minutes. Let cool slightly in the pan. Remove and place on a cooling rack to cool completely.
The original German metric measurements are 250 g unsalted butter, 250 g sugar, 500 g flour, and 125 ml milk.
Dust with powdered sugar or top with chocolate ganache if desired to serve.
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