Place the crushed Oreo cookies in a mixing bowl and add the softened cream cheese. Stir until the mixture forms a thick, even dough.

Divide the dough into four equal portions and roll each into a smooth ball. Place the balls on a baking sheet lined with parchment paper.

Insert one lollipop stick into the center of each ball, pushing it about halfway in. Chill the pops in the refrigerator for 10 minutes to firm up.

Melt the dark chocolate chips in a microwave-safe bowl in 30-second bursts, stirring between each until smooth. Dip each chilled pop into the melted chocolate, letting excess drip off, then return it to the baking sheet.

Melt the white chocolate chips the same way. Use a small spoon or piping bag to draw simple wing shapes on the surface of each coated pop. Let the chocolate set at room temperature before serving.