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. Start with the mixer on low speed and gradually increase to high. Pause to scrape the sides of the bowl.
Add vanilla extract and the remaining 4 cups of sugar, mix until combined, also starting on low and gradually increasing to high.
Add Oreo crumbs, 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.
For a firmer frosting, add more confectioner's sugar, ¼ cup at a time. For a softer frosting, add more milk or cream, one tablespoon at a time.
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.