In the bowl of an electric mixer, fitted with the wire attachment, beat together butter until smooth.
Slowly add 4 cups of powdered sugar and mix until smooth. Pause to scrape the sides of the bowl. Add vanilla extract, Oreo crumbs and remaining sugar, mix until smooth.
Add milk 1 tablespoon at a time, until you get a smooth, desired consistency.
Use immediately or cover and refrigerate up to three days. To use, once refrigerated, slowly allow to reach room temperature and then beat on low speed for just a few minutes, until the buttercream is smooth before using.