Preheat oven to 400 F
In a large bowl, use an electric mixer to beat butter and sugars together until light and fluffy.
Add the eggs to the butter & sugar and beat until light and fluffy again.
Add 3/4 C milk and 1/4 C peppermint schnapps to the same bowl as the butter & sugars, beat until thoroughly combined.
In a separate bowl, stir together flour, salt, baking powder, and cocoa powder.
Gradually pour the flour mixture into the sugar mixture. Beat until thoroughly combined.
Add in chocolate chips & 1 tablespoon crushed candy canes. Stir to combine thoroughly.
Use a piping bag (or zip lock) to transfer batter into a donut pan.
Bake at 400 F for about 10 minutes, or until fluffy and cooked through.
While baking, prepare the frosting. Combine powdered sugar, 3 tablespoons milk, and 1 tsp. peppermint schnapps (can substitute with peppermint extract for children). Stir well. Add more milk as needed in 1 tsp increments until the consistency is slightly thicker than glue.
Once the donuts are finished baking, allow them to cool *completely*. Dip each donut into the glaze and give it a little swirl to coat the entire "face" of the donut. Sprinkle with crushed candy cane. Enjoy!