Preheat the oven to 190C. Grease & flour the base and sides of an 7-inch cake tin; set aside.
Sift together the flour, baking powder & bicarb in a medium bowl. Whisk to combine; set aside.
In a different medium bowl, beat together the butter & sugar until fluffy and pale in colour. Beat the egg & the egg yolk into the mixture one at a time, mixing well between each addition. Beat in the vanilla extract, ensuring it is well combined.
Add half of the flour mixture into the butter mixture & beat on low speed until just combined. Add all of the buttermilk & beat until just combined. Add the remaining flour & beat until just combined, using a spatula to finish mixing everything together. If you notice a slight separation of the ingredients, don’t worry, this is a very forgiving recipe.
Pour the batter into the prepared tin and smooth out the top. Bake in the preheated oven for 35-40 minutes, or until golden brown all over & a skewer inserted into the centre comes out clean. Leave the cake to cool in the tin for 5-minutes before moving to a wire rack to cool completely.
While the cake cools, make the frosting. Place the chocolate in a heatproof bowl set over a medium saucepan filled with a few inches of simmering water (not touching) & cook until the chocolate has melted. Once melted, set aside.
In a large bowl, use an electric whisk to combine the icing sugar, butter, milk, & vanilla. Pour the melted chocolate into the bowl & beat until the frosting is smooth & light brown in color, scraping down the sides of the bowl as necessary.
When the cake has cooled, use an offset spatula to spread the frosting evenly over the top of the cake. Alternatively, transfer some of the frosting to a piping bag & pipe a line along the sides of the cake.
Slice cake into generous slices & enjoy wholeheartedly with a large cup of coffee.