Place 36 Oreo cookies into a food processor and pulse until they reach the consistency of fine, uniform crumbs.
Transfer the cookie crumbs to a mixing bowl, reserving 1 tablespoon for garnish, and add the softened cream cheese.
Blend the crumbs and cream cheese using a hand mixer or spatula until a cohesive, dark dough forms with no visible white streaks.
Portion the mixture and roll into 1-inch diameter spheres, placing them onto a baking sheet lined with parchment paper.
Transfer the tray to the freezer for 20 minutes to firm the spheres, which ensures the coating sets quickly and prevents crumbs from bleeding into the chocolate.
In a microwave-safe bowl, melt the white chocolate wafers in 30-second intervals, stirring between each, until the texture is smooth and fluid.
Submerge each chilled ball into the melted white chocolate using a fork, tap the fork against the side of the bowl to remove excess coating, and return to the parchment paper.
Melt the semi-sweet chocolate chips with the vegetable oil and drizzle over the set white chocolate shells.
Top with the reserved cookie crumbs and refrigerate for 30 minutes until the coating is fully crystallized.