In a stand mixer with the paddle attachment, beat the butter on medium, occasionally scraping the bowl, until very light and creamy, 3 to 4 minutes. With the mixer running on low, add the sugar about ¼ cup at at time, scraping the bowl as needed; once all the sugar has been added continue to mix on low until well combined and creamy, about 1 minute.
With the mixer still running on low, drizzle in the cream a few tablespoons at a time and beat until incorporated, about 10 seconds, before adding more. After about ½ cup of the cream has been added, the mixture will look curdy and broken; this is normal. Add the vanilla, then beat on medium, occasionally scraping the bowl, until the frosting is smooth, thick and fully emulsified, about 10 minutes. Increase to medium-high and continue to beat until the texture is light and fluffy, occasionally scraping the bowl, 2 to 3 minutes.
Chocolate 1-2-3 Frosting: In a small microwave-safe bowl, microwave 2 ounces finely chopped bittersweet chocolate on 50 percent power, stirring every 30 seconds, until melted and smooth. Follow the recipe to make the frosting. Add the melted chocolate to the finished frosting, then beat on medium until well combined and the frosting is light and creamy, 1 to 2 minutes, scraping the bowl as needed.
