Start with room temperature butter, soft enough to press a finger into but still holding its shape.
Beat the butter on medium speed until creamy and pale, about 2-3 minutes. Add cold heavy whipping cream and whip on high until light and fluffy, about 3-4 minutes.
Melt the bittersweet chocolate gently using a double boiler or microwave in short bursts, stirring frequently. Cool until pourable but not hot.
Sift together unsweetened cocoa powder, instant espresso powder, kosher salt, and powdered sugar in a separate bowl to remove lumps.
Pour cooled melted chocolate into the whipped butter mixture and beat on low until combined. Gradually add the dry ingredients, mixing on low speed and scraping sides as needed.
If frosting is too thick, add extra cold heavy cream a teaspoon at a time and whip briefly. If too thin, add more powdered sugar to thicken.
Use immediately to frost cakes or cupcakes, or layer in desserts like a Hot Cocoa Brownie Trifle.
