In a large bowl, combine the softened butter, cocoa powder and chocolate syrup. Beat on low speed with a handheld electric mixer until blended.
Gradually add the sugar and a couple of tablespoons of the milk and the teaspoon of vanilla.
Continue beating, adding milk as needed, until you get a smooth and glossy frosting.
Notes
If using unsalted butter, add a pinch or two of salt. I also recommend adding the powdered sugar gradually and taste testing after you've added the first 3 cups. You may not want all 4 cups.