Crush the chocolate sandwich cookies in a food processor until they resemble fine crumbs. In a mixing bowl, combine the cookie crumbs with melted butter, stirring until the mixture resembles wet sand. Firmly press this mixture into mini cupcake liners or silicone molds, shaping it into a solid base. Chill in the refrigerator for about 10 minutes to set while you prepare the filling.

In a medium bowl, beat the softened cream cheese with a hand mixer until it's smooth and creamy, ensuring there are no lumps. Gradually add the powdered sugar, peppermint extract, and vanilla extract to the cream cheese, mixing well until all ingredients are thoroughly incorporated and the filling is fluffy and well-blended.

Gently fold the melted white chocolate into the cream cheese mixture, being careful not to deflate it. Then, delicately incorporate the whipped cream until smooth and airy. Finally, mix in the crushed peppermint candies, leaving some aside for garnish.

Spoon the cheesecake mixture into each chilled cookie base, smoothing the tops for an even finish. Cover the bites with plastic wrap and refrigerate for at least 2 hours, allowing them to set properly before serving.

Just before serving, sprinkle the reserved crushed peppermint candies on top for extra crunch and festive flair. Carefully remove the bites from the liners or molds, and place them on a serving platter.