Preheat the oven to 350F degrees and line cookie sheets with parchment paper.
In a large bowl beat together the butter, shortening, white sugar & brown sugar until fluffy (about 2 minutes).
Add in the vanilla extract & peppermint extract, then mix in the eggs 1 at a time.
Turn the mixer down to low speed and mix in the flour, baking soda & salt. If the dough sticks to your fingers when you squeeze it between them - add in a little more flour 1 tablespoon at a time.
Mix in the crushed candy canes & white chocolate chips.
Form the dough into balls about 1 - 1.5 tablespoons in size* and place 2 inches apart on the lined cookie sheets.
Bake for 8-10 minutes, or until the tops look just set. Remove from the oven and place a few white chocolate chips on the top of each cookie (optional).
Cool on the cookie sheet for 10 minutes, then continue cooling on a wire rack.
*For larger cookies, form the dough into balls about 3 tablespoons in size and form the dough balls so that they're taller than they are wide. Bake for 12-14 minutes, or until the tops look just set.
To freeze the cookie dough, make the recipe through step 5 (without turning on the oven in step 1). Form the dough into balls and place them in a freezer bag. Remove the excess air, zipper close, and freeze for up to 2 months. When ready to bake, preheat the oven to 350F degrees and place the cookies on lined cookie sheets. Bake from frozen. They'll need an extra minute or 2.