Preheat oven to 350° Prepare a bundt pan by coating the inside of the pan with non-stick cooking spray. Dust the entire baking surface with flour and tap out the excess. Set aside.
In a large bowl, using a handheld mixer, mix together the butter and sugar on medium speed for 3 minutes.
Add the eggs one at a time and blend well into the sugar and butter mixture.
Next, add the peppermint extract and mix into the batter.
Sift together the flour, baking powder, and salt. Add to the wet ingredients and mix on low speed until just incorporated.
Add the milk and fully incorporate.
Stir in the crushed candy canes.
Transfer the batter to the prepared bundt pan.
Bake for 40 minutes. Test the cake to see if it has baked all the way through by inserting a toothpick into the center of the cake. If the toothpick comes out clean, the cake is done. If the toothpick comes out with batter on it, continue the baking process for a few more minutes. Test again.)
Remove from oven. Place the cake on a cooling rack and let set for 10-15 minutes before turning out onto the cooling rack to continue the cooling process.
For the Frosting:
When the cake has completely cooled, whisk together the confectioner's sugar, milk, and peppermint extract until smooth. Drizzle the glaze over the cooled cake and top with the remaining crushed candy canes.