Line a baking sheet with parchment paper and set aside.
In a food processor, pulse the cookies until obtaining fine crumbs (texture of flour). Add the cream cheese and continue pulsing until the mixture is well combined.
Using your hands, shape the cookie mixture into 1-inch balls. Then, make a hole in the center of each ball and insert one candy cane kiss into the middle. Roll the cookie again to reshape into balls. Arrange them in rows on the prepared baking pan and place in the freezer for about 20 minutes.
To make the dark chocolate glaze: Place both the chocolate and oil into a medium microwavable bowl. Melt the chocolate in the microwave in 30-second intervals (100% power), stirring between each interval, until fully melted. Stir in the vanilla. Using a spoon, dip the cookie balls in the melted chocolate, remove, and let them rest on a baking sheet on a rack in the freezer for about 20 minutes or until dark chocolate glaze solidifies.
After this, prepare the white chocolate glaze: Place white chocolate and shortening in a small microwave-safe bowl, heating in 30-second intervals and stirring. Repeat process until chocolate is completely melted. If you want a thinner glaze, stir in 1/4 cup of heated heavy cream to thin the mixture.
Using a teaspoon, spoon melted white chocolate glaze on top of each cookie ball, place coconut flakes on top of half of the cookies and decorate the other half with candy cane sprinkles, or any sprinkles of your choice. Let chocolate candy cane cheesecake cookies rest in the freezer for about 20 minutes until white chocolate glaze sets. Place chocolate candy cane cheesecake cookies carefully into bonbon cups and serve.