In a large bowl beat together sugar, butter and oil until light and fluffy. Next beat in eggs one at a time and the extracts.
In a separate bowl sift together flour, baking powder and salt. Stir into butter mixture to make a soft dough, before completely combined add the crushed candy cane.
On a floured surface pour the dough out and gently form it into a square, then divide it into four.
Gently shape each piece into 7 inch long logs. Place the logs onto a baking sheet lined with parchment paper or a Silpat approximately 2 inches apart.
Bake in a 325°F for 25 minutes until lightly golden and just slightly firm to the touch. Remove from the oven and allow to cool for 10 minutes.
Gently remove them from the baking sheet and place them on a cutting board. Using a sharp knife cut the logs into ½" pieces. Repeat with the remaining three logs.
Spread out slices upright on the baking sheet and return to the oven. Bake for 20 minutes until golden, firm and dry.