Preheat the oven to 180C/350F/Gas 4. Line a 12-cup muffin tin with muffin cases, and set aside.
Whisk together the flour, baking powder, baking soda, and salt. Set aside.
Whisk together the eggs. Add the sugar, and whisk until combined. Add the vanilla extract, butter, and yogurt, and whisk until combined. Fold in the dry ingredients.
Divide the batter evenly between the muffin cases, filling only 2/3 full.
Bake for 14 - 16 minutes, or until a toothpick inserted into the center comes out clean. Allow to cool for 5 minutes in the pan, before transferring them to a wire rack to cool completely before frosting.
For the Frosting
Using a handheld or stand mixer, beat together the butter and icing sugar until light and fluffy, then beat in the milk and vanilla extract until smooth, and spreadable.
Transfer the frosting to a piping bag, and frost the cooled cupcakes.
Notes
*Make your own cake flour! Measure out 1 and 1/2 cups (190g) of plain/all-purpose flour, remove 3 tablespoons, and replace with 3 tablespoons of cornflour/cornstarch. Sift well.Leftover cupcakes can be stored, covered tightly, in the fridge for up to 3 days. Frosted or unfrosted cupcakes can be frozen for up to 3 months. Thaw overnight in the fridge.Cupcakes can be made 1 day in advance, covered, and stored at room temperature. Cover the frosting, and store in the fridge until ready to use.