Preheat oven to 350 degrees F. Grease an 8×8 baking pan with butter or nonstick spray.
In a large bowl, combine melted butter with sugar and vanilla extract, whisking until combined and almost smooth. Whisk in each egg one at a time, stirring until a smooth batter forms. Add in flour, cocoa powder, baking soda and salt, stirring until combined. Fold in chocolate chips. Spread batter in the 8×8 baking dish and bake for 25-30 minutes until set. Remove and let cool.
While brownies are cooling, add powdered sugar, butter, milk, vegetable oil, vanilla and peppermint extracts to the bowl of an electric mixer. Beat until smooth and creamy. Pour over brownies and spread in an even layer with a spoon or spatula. Place in the refrigerator until set, about 30 minutes.
To make ganache, heat heavy cream until warm and pour it over chopped chocolate. Stir for a few minutes until totally combined, smooth and creamy. Spread over the top of the peppermint layer or cut brownies first and spoon over top. I love these refrigerated!