Preheat oven to 350F.
In food processor, pulse cookies until fine crumbs form.
Add butter and pulse until well-combined.
Press cookie crumbs evenly into the bottom of a 10” springform pan. Sprinkle 1 Tbsp of crushed candy cane over the crust.
In KitchenAid, beat cream cheese until smooth.
Add sour cream and sugar and stir on medium-low until well-combined, pausing to scrape down sides.
Add eggs, one at a time, beating until combined after each addition and scraping down the sides of the bowl after each addition.
Add vanilla and stir until combined.
Split the batter by transferring half to a clean bowl.
To one half, add ¼ cup crushed candy canes, peppermint extract, and red food dye until desired color is reached (caution: too much dye can give the cheesecake a bitter flavor. If not using color, there is no need to divide the batter, simply stir the crushed candy into the original bowl).
Layer the cheesecake over the prepared crust, alternating colors (first an even layer of the white batter, using about 1/3 of that batter, then spread about 1/3 of the red batter over that, repeating until all batter is used).
Bake on 350 for 40-45 minutes, until center is set.
Allow to cool at room temperature completely before transferring to fridge and allowing to chill 6 hours (or overnight).
Once chilled, prepare ganache by heating chocolate and heavy cream in small saucepan over medium-heat, stirring frequently until chocolate is melted and the mixture is smooth.
Remove from heat and allow to cool 2-3 minutes. Pour over cheesecake, lightly nudging mixture over the edges as desired. Sprinkle with the 2 Tbsp crushed candy canes. Allow ganache to harden in fridge for at least 15 minutes before cutting and serving.