Preheat oven to 350 degrees. In a large mixing bowl whisk together flour, brown sugar, granulated sugar, cocoa powder, baking powder, baking soda and salt. Add in vegetable oil, milk, egg, vanilla extract and peppermint extract and beat with an electric mixer on low speed for 2 minutes. Stir in hot water, stir until well combined. Add in sour cream and mix until well blended. Fill paper lined muffin cups ¾ full and bake cupcakes in preheated oven for 17 – 19 minutes, until toothpick inserted in center of cupcake comes out clean. Remove from oven and allow to cool several minutes in muffin pan before transferring to a wire rack to cool. Cool on a wire rack for 30 minutes.
Once cupcakes are cool, spread about 1 teaspoon cooled milk chocolate ganache over each cupcake. Place cupcakes in a 13x9 inch baking dish, cover with plastic wrap and chill about 10 mintues while you make the peppermint cream cheese frosting.
Pipe each chocolate ganache covered cupcake with peppermint cream cheese frosting and sprinkle cupcakes with crushed candy canes.
For the Milk Chocolate Ganache
Combine milk chocolate chips and cream in a microwave safe bowl and microwave mixture on 50% power in 30 second intervals, stirring after each interval until melted and smooth. Cool mixture in refrigerator for about 10 minutes (basically until it’s a spreadable not so drippy consistency).
For the Peppermint Cream Cheese Frosting
In a large mixing bowl, using an electric mixer, whip together butter and cream cheese until fluffy, about 1 minute. Stir in vanilla and peppermint extract. Slowly add in powdered sugar and mix until well combined and fluffy.