In the bowl of a food processor, process the Oreos to make very fine crumbs. (You can also put them in a zip-top plastic bag and crush them very finely with a rolling pin.)
In the bowl of a stand mixer fitted with a paddle attachment, beat the butter on medium speed for about 2 minutes until creamy.
Add the vanilla extract, salt, and half of the powdered sugar. Beat on low speed for 30 seconds, just until combined.
Add 1 tablespoon of heavy cream and the remaining powdered sugar. Beat on low speed for 30 seconds just until combined. Increase the speed to medium and beat for 2 minutes until light and fluffy.
Add the pulverized Oreos and beat on medium speed for 30 seconds to 1 minute until well combined. (If the buttercream looks dry and not creamy, add the remaining heavy cream, 1 teaspoon at a time and mix to combine.)
