Preheat the oven to 350F degrees (180C). If your oven is a convection oven, be sure that the temperature is reduced to 325F (160C) degrees (some convection ovens to this automatically).
Line the 6 middle cavities of a regular-sized muffin tin with muffin papers.
In a medium bowl using a hand-held electric mixer, beat the egg and sugar for about 5 minutes or until the mixture is very pale in color and has significantly increased in volume.
Sprinkle the flour, baking powder and salt over the eggs and gently whisk in the dry ingredients.
Add the butter and milk to a liquid measuring cup. Microwave in 30-second increments until the butter is melted. 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. You should end up with 6 cupcakes.
Bake in the preheated oven for 18-20 minutes or until the tops look set and are slightly firm/springy to the touch, or an inserted toothpick comes out clean.
Cool the cupcakes for 10 minutes in the pan, then remove from the pan and continue cooling on a cooling rack.
Frosting
In a small bowl, beat the butter until smooth.
Add in the salt and vanilla extract. Starting with the mixer on low speed, beat in 1 cup powdered sugar.
Mix in the rest of the powdered sugar about ½ cup at a time, alternating with a tablespoon of milk or cream until the desired sweetness and thickness is reached. Optionally, mix in a few drops of food coloring.
Either frost the cupcakes with a knife, or transfer the frosting to a piping bag and frost. I used a piping bag and a 1M tip.
Notes
I recommend using a bowl and hand-held mixer instead of a stand mixer for this recipe. Because there isn't a lot of batter, you will need to constantly scrape down the sides of the bowl with a stand mixer.
When measuring flour, whisk it first. Then spoon into a dry measuring cup and level off the top. Or use a scale. ⅔ cup flour weighs 83 grams.
The frosting recipe provided makes a lot of frosting - enough to pipe each cupcake with a very, very thick amount. If you'd like less frosting, divide the frosting reicpe in half. You'll need:
¼ cup unsalted butter
1 cup powdered sugar
tiny pinch of salt
¼ teaspoon vanilla extract
1 tablespoon of milk or cream
Store unfrosted cupcakes in an airtight container at room temperature for up to 3 days. Frosted cupcakes can be stored in an airtight container at room temperature for up to 1 day or in the fridge for up to 4 days. Remove cupcakes from the fridge 30 minutes before enjoying. If your kitchen is warm, store cupcakes in the fridge.
Nutrition information is an estimate only and based on 1 cupcake with frosting, assuming all the frosting is used and divided between 6 equal-sized cupcakes (without the frosting recipe divided in half).