Begin by ensuring that the butter is softened. It should be at room temperature for easier blending.
In a mixing bowl, add the softened butter and beat it with a hand mixer or in a stand mixer at medium speed until it becomes creamy and smooth.
Gradually add the powdered sugar, one cup at a time, to the butter while continuing to mix on low speed. Ensure each addition of powdered sugar is well incorporated before adding more.
Once all the powdered sugar has been added and mixed in, sift the unsweetened cocoa powder into the bowl with the butter-sugar mixture.
Pour in the milk and add the vanilla extract to the bowl.
Begin mixing on low speed to incorporate the cocoa powder, milk, and vanilla extract into the butter-sugar mixture. Scrape down the sides of the bowl with a spatula to ensure everything is well combined.
Increase the mixer speed to medium and beat the frosting for an additional 2-3 minutes until it becomes light, fluffy, and smooth. If the frosting seems too thick, add a little more milk (a teaspoon at a time) until it reaches your desired consistency. If it's too thin, add more powdered sugar (a tablespoon at a time).
Once the chocolate buttercream frosting has reached the desired consistency and texture, it's ready to use!