Line a baking sheet with parchment paper and set aside.
Since white chocolate hardens so quickly, it's easiest to work in several batches: In a microwave safe bowl place 1/2 cup of white chocolate chips with 1/4 tablespoon vegetable oil in the microwave.
Microwave for 30 seconds, stir, and microwave for another 25 seconds. Stir until melted or return to the microwave for a little longer. Add more vegetable oil if needed. Be patient when melting and stir well in between bursts to avoid burning the chocolate.
Dip one end of the lollipop stick into the melted chocolate and press that side into the cream side of the oreo. Place the other half of the oreo on top and gently press and hold. Let harden completely.
Spoon the melted white chocolate over the oreo pop evenly. Gently tap the oreo pop on the edge of the bowl to get the chocolate to cover the oreo evenly. You may want to do a few coats of the chocolate to make sure it is throughly white.
Place the dipped cookies on prepared baking sheet.
Place all the leftover white chocolate (make sure it is still very melted -- place in microwave for another 15 seconds if needed) into a small plastic bag (or a frosting bag fitted with a #2 tip)
Cut the very edge corner off of the plastic bag and then pipe the melted white chocolate over the cookies to form the "bandages" of the mummy.
Secure 2 sprinkle eyes on the wet chocolate.