Preheat oven to 350F. Spray two doughnut pans with baking spray.
In a large bowl, whisk together the flour, sugar, baking powder and salt.
In a small bowl, whisk together the egg, milk, melted butter and extracts. Add to dry ingredients and stir until combined.
Spoon batter into baking pans, filling them each about three-quarters full. Bake for 15 – 18 minutes, until a toothpick comes out clean. Let cool for 5 minutes then transfer to cooling rack.
To make the glaze, stir together the powdered sugar, heavy cream and extracts. Dip the doughnuts in the glaze them place back on cooling rack. Immediately sprinkle with crushed candy canes.