I really like these cupcakes. They remind me of the ones I am more familiar with from my childhood. The ones I am thinking about came with a thick sticky and often flavoured icing and were a real treat from the supermarket in a box of 6.  We iced these with just an icing sugar and hot water mix, oh, and green food colouring. I am not fond of butter icing.
Miss Muffin made these and was very proud. She needed minimal assistance and reassurance from me.
I really like this cookbook and would recommend that you need it.
The Hummingbird Bakery cookbook p14
For the cake-
120g plain flour
140g caster sugar
1 ½ tsp baking powder
a pinch of salt
40g unsalted butter, at room temperature
120ml whole milk
1 egg
¼tsp vanilla extract
Preheat the oven to 170°C (325°F) Gas 3.

Put the flour, sugar, baking powder, salt and butter in a freestanding electric mixer with a paddle attachment (or use a handheld electric whisk) and beat on slow speed until you get a sandy consistency and everything is combined. Gradually pour in half the milk and beat until the milk is just incorporated.
Whisk the egg, vanilla extract and remaining milk together in a separate bowl for a few seconds, then pour into the flour mixture and continue beating until just incorporated (scrape any unmixed ingredients from the side of the bowl with a rubber spatula).
Continue mixing for a couple more minutes until the mixture is smooth. Do not overmix.
Spoon the mixture into the paper cases until two-thirds full and bake in the preheated oven for 15-20 minutes, or until light golden and the sponge bounces back when touched.
A skewer inserted in the centre should come out clean. Leave the cupcakes to cool slightly in the tray before turning out onto a wire cooling rack to cool completely.