Place your butter in the microwave and melt, about 30 seconds. Allow to cool for a few minutes. Add in your eggs and vanilla to the melted butter and whisk together.
Add your butter mixture to your flour mixture, with the buttermilk, and stir until just combined. Spoon the mixture into prepared cupcake liners, about 3/4 full.
Bake your cupcakes for 18-20 minutes or until a toothpick inserted in the middle comes out almost clean. Allow to cool in the cupcake tin for 5 minute before transferring to a wire rack to cool completely.
In a large bowl with an electric whisk, beat your butter on medium speed until smooth and creamy. Add half of your icing sugar and two tablespoons of milk and continue to whisk until combined.