Line a baking sheet with parchment paper. Pulse the graham crackers in a food processor until finely ground but not powdery. Transfer 1/3 cup of the crumbs to a large bowl. Add the cookie butter to the remaining crumbs in the food processor and pulse, scraping down the side of the processor if needed, until combined and the mixture starts forming a ball. Add to the bowl with the graham cracker crumbs and mix until combined.
Roll tablespoonfuls of dough into 1-inch balls and arrange on the prepared baking sheet. Cover with plastic wrap and refrigerate until cold and firm, at least 1 hour or overnight.
Combine the white chocolate chips and coconut oil in a large microwave-safe bowl. Microwave in 30-second intervals, stirring, until smooth. One at a time, gently drop each cookie into the melted chocolate, turning to coat completely. Remove with a fork, allowing the excess chocolate to drip off, then return to the baking sheet. (If the chocolate gets too thick, return to the microwave.) Decorate with nonpareils. Let set, 30 minutes.