Preheat the oven to 160°C (conventional oven). Line a 12-hole cupcake tin with navy cupcake cases and set aside.
Place the dark chocolate and one of the 45g portions of butter into a medium-sized microwaveable bowl. Melt in the microwave on the lowest setting, in 1-minute bursts, stirring between each burst, until smooth. Repeat this process with the white chocolate and the remaining 45g of butter, in a separate bowl. Set both bowls aside to cool slightly.
Once cooled, add the 30g portion of caster sugar and all of the light brown soft sugar to the dark chocolate mixture. Stir well to combine. Add the remaining 20g portion of caster sugar and all of the dark brown soft sugar to the white chocolate mixture. Stir well to combine.
In a large jug, whisk together the oil, milk, eggs, sour cream and vanilla extract. Add half of this mixture to each bowl and mix well to combine (see Note 4).
Add the coffee, dissolved in the hot water, to the dark chocolate mixture and mix to combine.
Sift the 90g portion of self-raising flour into the dark chocolate mixture, along with the cocoa powder and a pinch of salt. Then, sift the remaining 100g of self-raising flour and another pinch of salt into the white chocolate mixture. Stir both mixtures separately, until the dry ingredients are just incorporated.
Transfer each batter to a separate jug, then pour both batters simultaneously into each cupcake case, to give the half-and-half effect. Fill each case about 3/4 of the way full, then bake in the preheated oven for 25-30 minutes, until they just about spring back when touched.
Once baked, remove the cupcakes from the tin immediately, to prevent the cases from becoming greasy. Place onto a wire rack and set aside to cool completely before decorating.