Preheat the oven to 350 degrees F. Line a baking sheet with parchment paper or a nonstick baking mat.
Place the butter, granulated sugar and brown sugar in the bowl of a mixer. Beat until light and fluffy, about 3 minutes.
Add the eggs, vanilla extract and peppermint extract (if using). Beat until combined.
Add the flour, salt, pudding mix and baking soda to the bowl. Mix on low speed until just combined.
Fold in 3/4 of the Oreos, white chocolate and candy canes.
Take 2 tablespoons of dough and roll it into a ball. Repeat with remaining dough.
Place the balls of dough 2 inches apart on a baking sheet. You will need to bake the cookies in batches.
Press the remaining Oreos, candy canes and white chocolate onto the tops of the balls of dough.
Bake the cookies for 10-12 minutes or until light brown at the edges.
Cool the cookies on the pan for 10 minutes, then transfer to a cooling rack.
Repeat the baking process with the remaining dough.
Serve immediately or store in an airtight container for up to 4 days.