Melt white and dark chocolate in separate bowls, using a double boiler or microwave, and transfer the dark chocolate to a piping bag.
Gently twist a popsicle stick halfway into the cream center of each Oreo.
Dip each Oreo into the melted white chocolate, tilting and turning until fully coated.
Place coated pops on a parchment-lined baking sheet for flat backs or in a cake pop stand for smooth all-around coating.
Let the pops set at room temperature for 15–20 minutes or chill in the fridge for 5–10 minutes.
Pipe on Jack’s face with the dark chocolate, adding eyes, nostrils, and a stitched smile.
Allow the details to set, then serve, wrap as favors, or display on your dessert table.