Prepare a large sheet pan by lining it with parchment paper and set aside. Gently separate the oreos by slowly twisting them apart. (Some will break, it's okay, just try to be gentle)
Separate the white chocolate into 3 parts (this is to keep it from getting hard while you decorate) and place each section in a microwave safe bowl.
Add about 1/2 teaspoon vegetable oil or shortening into each bowl of white chocolate chips (more if needed to thin it even more).
Melt in 20 second bursts in the microwave (Microwave 20 seconds, stir 20 seconds, etc.) 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. Press the tines of the plastic fork into the oreo creme.
Place the other half of the oreo on top and gently press and hold.
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 white-chocolate oreo pops on the prepared tray and (before the chocolate hardens) press a candy melt iIf needed, use a sharp serrated knife to cut off the very front of the candy melt so the surface will hold the edible candy eye) into the center of the oreo pop. Dab some more melted chocolate on the back of the edible eye and adhere that to the candy melt.
Allow to completely harden at room temperature.