Preheat your oven to 350 degrees. Grease bottom and side of 9-inch springform pan.
Process the cookies in a food processor until finely ground, about 30 seconds. Add the melted butter and pulse until combined, 6 to 8 pulses. Transfer the crumb mixture to prepared pan and use your hands to press the crumb mixture evenly into the bottom of the pan. Tip: Using the bottom of a dry measuring cup, firmly pack crust into pan. Bake until fragrant and set, about 10 minutes. Let cool completely on wire rack.
For the filling: Reduce the oven temperature to 300 degrees. In a stand mixer fitted with the paddle attachment, beat the cream cheese and sugar until smooth, about 1 minute, scraping down the bowl as needed. Add the eggs, one at a time, beating just until incorporated, about 30 seconds total. Scrape down the sides of bowl. Add the sour cream, vanilla, peppermint extract, and beat just until combined, about 15 seconds. Add the chopped white chocolate and the peppermint bits and fold into the cheesecake quickly (you want to mix quickly and minimally because the peppermint bits will begin to tint the batter pink).
Pour the cheesecake mixture over the crust. Lift and gently tap the pan on the counter to release any air bubbles. Pop any air bubbles that have risen to surface.
Bake the cheesecake until the edges are set and center jiggles slightly when shaken and (it Bake until edges are just golden and center jiggles slightly when pan is gently shaken, about 1 hour 20 minutes to 1 hour 30 minutes. Run a knife around edge of pan rim. Transfer to a wire rack and let cool completely, about 2 hours. Refrigerate, uncovered, until completely cold, about 6 hours or overnight.
To unmold the cheesecake, run a small sharp knife between around the sides of the pan, then unlock and release the sides. Optional: To loosen the crust from the pan, slide a thin metal spatula between the crust and the bottom, then slide the cheesecake onto your serving platter.For the topping, in a large bowl, beat the cream, vanilla, and powdered sugar with an electric mixer (handheld or stand mixer) until stiff peaks form. Spread half of the whipped cream over the cheesecake and spoon the remaining half into a large plastic bag, snip off one bottom corner of the bag with scissors and pipe the whipped cream in small circles around the edges of the cake. Sprinkle the top with more crushed peppermint candies.
Let the cheesecake stand at room temperature for 30 minutes before serving. It can be covered and refrigerated for up to 4 days.