Preheat oven to 350°F (175°C) and grease and flour two 9-inch round cake pans.

In a mixing bowl, beat cream cheese and granulated sugar until smooth. Add the egg and vanilla extract; mix well and set aside.

Melt the German chocolate and butter together in a saucepan over low heat, then cool slightly.

In a separate bowl, combine granulated sugar, brown sugar, and egg yolks; beat until light and fluffy.

Stir in the melted chocolate mixture and vanilla extract.

In another bowl, whisk flour, baking powder, baking soda, and salt, then gradually add to the chocolate mixture, alternating with buttermilk.

Whip the egg whites into stiff peaks and gently fold into the batter.

Pour half the cake batter into each prepared pan. Spoon half of the cheesecake mixture on top, followed by the remaining cake batter.

Bake for 30-35 minutes or until a toothpick inserted comes out clean. Cool the cakes in the pans for 10 minutes, then transfer to a wire rack to cool completely.

Melt the German chocolate and butter in a saucepan, then cool slightly.

Whisk together powdered sugar, milk, and vanilla extract, then fold in the cooled chocolate mixture.

Place one layer on a serving platter and frost with half of the frosting. Top with the second layer and use remaining frosting on top.