Place the Oreo cookies in a food processor and grind them into fine crumbs.
Add the softened cream cheese to the crumbs and blend until a thick, sticky dough forms.
Transfer the mixture to a bowl and mix with a spatula until smooth.
Line a baking sheet with parchment paper.
Scoop about 1½ tablespoons of the mixture for each ball and roll it into a smooth round shape.
Place the balls on the prepared baking sheet and chill in the refrigerator or freezer for about 30 minutes to firm up.
Melt the dark chocolate coating until smooth, then dip about half of the chilled balls into it, tapping off any excess chocolate.
Immediately sprinkle the dipped balls with Christmas sprinkles before the chocolate sets.
Melt the white chocolate coating until silky, then dip the remaining Oreo balls into it.
Add sprinkles to these balls as well, pressing gently so they stick.
Return all the coated balls to the lined sheet and chill until the chocolate is fully set.