Preheat the oven to 180°C (350°F). Grease and line a 20cm (8-inch) round cake tin.
In a saucepan over low heat, melt the milk chocolate and butter, stirring frequently until smooth. Once melted, remove from heat and add the milk, vegetable oil, and vanilla extract. Stir until combined.
In a large bowl, sift together the flour, caster sugar, brown sugar, cocoa powder, baking soda, baking powder, and salt.
Add the wet mixture (chocolate-butter-milk mix) to the dry ingredients, mixing until smooth. Beat in the eggs, one at a time.
Slowly pour in the boiling water, mixing gently. The batter will be thin.
Pour the batter into the prepared cake tin. Bake for 45-50 minutes, or until a skewer inserted into the center comes out clean. Let the cake cool completely.
While the cake cools, melt the milk chocolate for the frosting in a heatproof bowl over a saucepan of simmering water or in the microwave in 30-second bursts. Once melted, add the heavy cream and mix. Sift in the icing sugar and cocoa powder, adding milk as needed until smooth and spreadable.
Once the cake has cooled, frost it with the milk chocolate frosting. Smooth it out with a spatula. Serve and enjoy!