Preheat oven to 350 degrees. Grease and flour a bundt or tube (angel food cake) pan and set aside.
Cream butter in a mixer or food processor until smooth and a slightly lighter shade of yellow. Add eggs, sugar, extracts, and milk and continue mixing until uniform.
In another bowl, mix together flour, sea salt, and crushed peppermint candy.
Add dry ingredients to wet mixture and beat until uniform and smooth. It may be necessary to hand stir a couple of times in order to ensure no pockets of flour remain.
Spread batter into prepared pan and bake on middle rack of oven for about an hour and 10 minutes or until a toothpick inserted into multiple sections of the cake comes out clean.
Remove cake from pan. Cool completely then sift powdered sugar over top before serving.