In a food processor on high, pulverize whole Oreos together until cookies are reduced to crumbs. Set aside.
In a stand mixer bowl with whisk attachment, whisk softened butter on high until light and creamy, about 3-4 minutes. Turn mixer to slow and add in powdered sugar a half cup at a time. Once sugar is incorporated, crank speed to high until well blended. Continue adding the rest of sugar in this manner.
Mix in vanilla, salt, and heavy cream on high until you've reached the desired consistency. If you want the frosting to be stiffer, add more powdered sugar. Fold in Oreo crumbs with a spatula until combined.