Use a food processor to crush cookies into fine crumbs.
Add all but 2 tablespoons crushed cookies to a medium bowl. Add cream cheese and vanilla and stir until evenly combined.
Line a baking sheet with parchment paper. Using a small cookie scoop, form mixture into small balls. Place on prepared baking sheet and freeze until slightly hardened, about 30 minutes.
A few minutes before taking the frozen balls out of the freezer, melt the white chocolate and coconut oil: Add the white chocolate and coconut oil to a microwavable bowl, and microwave for 1 minute. Give it a stir. It may be melted at this point, if not, return to microwave in 30-second intervals.
Dip the frozen balls in melted white chocolate/coconut oil until coated, and return to baking sheet. Drizzle with semisweet chocolate. Freeze until chocolate hardens, about 15 minutes.
