Place the chopped chocolate in a microwave-safe bowl and microwave in 30-second increments on 50% power, stirring after each, until the chocolate is melted and smooth. Set aside to cool to room temperature.
Meanwhile, using the whisk attachment of your stand mixer, whip the butter on medium-high speed for 5 minutes, stopping to scrape the bowl once or twice.
Reduce the speed to medium-low and gradually add the powdered sugar. Once all of the powdered sugar is incorporated, add the vanilla, mixing until incorporated. Add the melted chocolate and whip at medium-high speed until light and fluffy, about 2 minutes, scraping the bowl as needed to incorporate all of the chocolate.
Use immediately or cover with plastic wrap and keep at room temperature for up to 4 hours before using. The frosting can be refrigerated, covered, for up to 4 days. Bring to room temperature and re-whip before using. The frosting can also be frozen in an airtight container for up to 3 months. Thaw in the refrigerator, then bring to room temperature before using.
Notes
Nutritional values are based on one cup of frosting