Crush the Golden Oreos into fine crumbs. Mix with melted butter and press into a 9x13-inch pan. Refrigerate for 10 minutes.
In a mixing bowl, beat cream cheese, sugar, and 2 tbsp milk until smooth. Fold in half of the Cool Whip and spread over the crust.
Whisk the vanilla pudding mix with 2 1/2 cups milk and peppermint extract. Add red food coloring until a light pink shade is achieved.
Spread the pudding layer over the cream cheese layer. Refrigerate for 10 minutes.
Top with remaining Cool Whip and sprinkle with holiday sprinkles and white chocolate shavings.
Chill for at least 4 hours before serving.