Cream together the butter, oil and sugar until pale. This will take a few minutes. Add in the eggs one at a time, mixing well between each one. Turn the whisk right down, if using an electric one, and add in the milk. Sift in the dry ingredients and fold through the mix.
Grease the mini cupcake tray, and place a teaspoon amount of the mix into each of the cake holes. Flatten slightly so the mix is evenly spread and place in the hot oven for around 12 minutes until fluffy and cooked through.
Whilst the cupcakes are baking, make the frosting. Whisk the butter with an electric whisk until very pale. Then on a low speed, whisk in the icing sugar and once combined, whisk in the cream cheese till just mixed. Place in a piping bag with a round hole nozzle attached or simple cut off the end of the piping bag.
Once the cakes are out and cooled, trim the top if any are particularly domed, then pipe a spiral shape on the top of the cakes. Start from the outside and slowly work your way into the centre. Trim the top of the strawberry and place on top. Finish with a blob of frosting on the top.