Prepare and bake your cookies! Let them cool completely. My batch made 34 cookies so I had about 17 sandwiches.
In a medium bowl, add in the butter and powdered sugar. Beat on low until most of the sugar is incorporated.
Add in the peppermint oil and milk. Start with 2 tablespoons and add the additional if your frosting is still too think. Mix on high until light and fluffy about 1-2 minutes.
Stir in the peppermint crunch with a spatula.
Fill the cooled cookies.
Notes
If you don't have peppermint oil such as LorAnn's Oils, use about ¼ tsp. to ½ tsp. of peppermint extract. The oils are much stronger than the extracts.