Add room temperature butter to a large mixing bowl or the bowl of a stand mixer fitted with a whisk or paddle attachment. Whip the butter for 5 minutes on medium-high speed, scraping down the sides occasionally, until the butter is light, fluffy, and pale in color.
Add one half of the powdered sugar and mix on the lowest speed setting until fully combined. Add remaining powdered sugar and continue to mix on low until incorporated.
Add instant espresso powder, vanilla extract, and salt and mix on low until combined.
Slowly drizzle in the heavy cream while mixing on low speed. Scrape the sides of the bowl occasionally to ensure the frosting is well mixed.
Once the heavy cream is added, turn the speed on the mixer to medium-high and mix for an additional 3 minutes until smooth. If there are still instant espresso powder granules present, turn the mixer on low speed and continue to mix until they are fully dissolved.