Preheat the oven to 350 degrees F (175 degrees C). Grease an 18-cup mini muffin tin or line with cupcake liners.
Sift flour, baking powder, and salt into a bowl.
Whip butter and sugar in a separate bowl with an electric mixer until fluffy. Mix in egg and vanilla extract. Add flour mixture and milk; whip until just combined. Fill the prepared muffin cups 3/4 full with batter.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 10 to 14 minutes. Cool in the tin for 5 minutes, then transfer to a wire rack and let cool completely, about 20 minutes.
Meanwhile, whip powdered sugar, butter, and vanilla for frosting in a bowl until well combined. Frost cooled cupcakes.
This recipe makes 18 mini cupcakes but you can easily double the recipe. Make sure you use pure vanilla and not imitation.
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