In a mixing bowl, beat the softened unsalted butter with an electric mixer on medium speed until creamy (about 1-2 minutes).
Sift the cocoa powder and powdered sugar together to remove any clumps.
Gradually add the cocoa powder and powdered sugar mixture to the butter, mixing on low speed until combined.
Add the milk and vanilla extract to the mixture, and continue to beat on medium speed until the frosting is smooth and creamy (about 2-3 minutes).
If the frosting is too thick, add more milk, one tablespoon at a time, until you reach the desired consistency.
Once ready, use a spatula to spread the frosting over your cooled cakes or cupcakes, or pipe it for decorative purposes.
Make sure the butter is at room temperature for easier mixing.
You can store leftover frosting in an airtight container in the refrigerator for up to one week. Allow it to come to room temperature and rewhip before using again.