Beat butter and cream cheese together, on medium-high speed, until smooth, for a couple of minutes.
Lower the speed to low and beat in powdered sugar and vanilla extract.
Turn up the speed back to medium-high and beat for another minute, until the frosting is light, smooth, and fluffy.
For chocolate frosting:
Melt chocolate in the microwave on "melt" setting. If melting setting is not available, melt at half the power for 45 seconds, stir and melt for 30 more seconds. Continue to microwave in 30 second increments at half the power and stirring in between until the chocolate is melted. Let it cool for a couple of minutes
Add cocoa powder at the same time as powdered sugar. Scrape sides and bottom of the bowl.
Raise the speed to medium-high and drizzle in melted chocolate while frosting is beating until all combined.