In a microwave-safe bowl, heat the semisweet chocolate in the microwave in 15 second intervals, stirring in between each interval, until the chocolate is melted and smooth. Set aside to cool.
In a small mixing bowl, stir together the black cocoa powder and hot water until combined and smooth. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment or in a large mixing bowl with an electric hand mixer, whip the unsalted butter for 5 minutes until light, pale, and fluffy.
Add in the powdered sugar, corn syrup, vanilla extract, and salt. Mix on low speed until well combined. Turn the speed of the mixer to medium speed and whip the frosting for 2 minutes.
Add in the cooled melted chocolate and black cocoa mixture, and mix on low speed until smooth. Scrape the sides and bottom of the bowl as needed. Turn the mixer to medium-low speed and mix the frosting for 2 to 3 minutes until it is smooth and creamy.