Preheat the oven to 350F. Line 12 cup muffin/cupcake tin with liners.
Combine butter and sugar in the bowl of your stand mixer fitted with the paddle attachment. Cream together on high speed until light and fluffy, about 2 minutes, scraping down the sides with a rubber spatula as needed. Add in the eggs, milk, and vanilla then mix until well combined and smooth. Change speed to low then add in the flour, cocoa powder, baking powder, and salt until well combined.
Divide batter between cupcake liners (they should be about ½ full) and bake for 20-24 minutes or until a toothpick inserted in the center comes out clean. Remove cupcakes from the oven then allow to cool completely on a cooling rack.
While the cupcakes are cooling, make your buttercream!
Add room temp butter to the bowl of your stand mixer fitted with a paddle attachment then beat on medium speed until creamy, about 2 minutes. Add 4 ½ cups powdered sugar, oreo cookie crumbs, heavy cream, vanilla and peppermint extract, green food coloring, and a healthy pinch of salt to the bowl then medium-low speed for about 2 full minutes or until thick and creamy, scraping down the sides of the bowl with a rubber spatula as needed. [Add up to ½ cup more powdered sugar if frosting is too thin or another tablespoon of heavy cream if frosting is too thick.]
Pipe buttercream onto cooled cupcakes and enjoy!