In a small bowl, whisk together the instant pudding mix and cold milk (or heavy cream). Whisk for about 2 minutes until it's smooth and starts to thicken. Set aside.

In the bowl of a stand mixer with the paddle attachment, or in a large bowl with a hand mixer, beat the softened butter on medium-high speed for 5-7 minutes. Scrape down the bowl occasionally. The butter should become very light, pale, and fluffy.

Reduce the mixer speed to low and gradually add the sifted powdered sugar, mixing until just combined. Add the vanilla extract and salt.

With the mixer still on low, add the thickened pudding mixture to the butter one spoonful at a time. Once all the pudding is added, increase the speed to medium-high and beat for another 3-4 minutes until the frosting is light, airy, and completely smooth. Use immediately or store as directed.