Melt the Butter: Begin by melting the butter in a large bowl in the microwave or over a double boiler until it is completely smooth.
Mix Dry Ingredients: Sift the cocoa powder and powdered sugar into the melted butter to avoid lumps, ensuring a smooth texture.
Combine Ingredients: Start mixing at a low speed using an electric mixer to incorporate the dry ingredients with the melted butter. Gradually add the milk and vanilla extract, and continue mixing. Increase the speed to medium as the mixture becomes cohesive.
Adjust Consistency: Continue to mix until the frosting is smooth and creamy. If the frosting is too thick, add a bit more milk a tablespoon at a time until the desired consistency is achieved.