Preheat the oven to 180C and grease a 27cm bundt tin with butter.
In a mixing bowl, combine butter and oil using the electric whisk. Add the eggnog, whisk. Add the eggs (one at a time) followed by the sugar and vanilla extract, whisk again.
Stir in flour, cinnamon, nutmeg, baking powder, and baking soda. Pour the batter into the bundt tin.
Bake for 40-45 minutes. Let it cool down completely before turning it out on a wire rack.
Making the white chocolate icing:
In a small saucepan, heat the heavy cream on medium heat. Pour it over the chocolate and whisk until chocolate melts. Then pour the chocolate icing on top of the eggnog bundt cake. Slice the cake and serve.