Preheat the oven to 350F degrees (180C). If using a convection oven, reduce the temperature to 325F (160C).
Line the 6 middle cavities of a muffin tin with muffin papers.
In a medium bowl, beat the egg and sugar for about 5 minutes until pale and increased in volume.
Sprinkle the flour, baking powder, and salt over the eggs and gently whisk in.
Melt the butter and milk in a measuring cup in the microwave, then whisk in the vanilla extract.
Whisk the warm milk mixture into the batter until smooth.
Spoon the batter into the cupcake liners, filling each about ⅔ to ¾ full.
Bake for 18-20 minutes until the tops are set and a toothpick comes out clean.
Cool the cupcakes for 10 minutes in the pan, then transfer to a cooling rack.
For frosting, beat the butter until smooth, then add salt and vanilla extract.
Gradually mix in powdered sugar and milk or cream until desired sweetness and thickness is reached.
Frost the cupcakes with a knife or piping bag.