Heat the white chocolate and cream together in a large heatproof bowl set over a pot of simmering water and stir until smooth (it will be thick). Remove the pan from the heat and stir in the cookie butter and unsalted butter until smooth.
Cover the bowl with plastic wrap and refrigerate until firm (2 hours or overnight).
Use a tablespoon to scoop out some of the mixture and quickly roll it into a ball. Place on a baking sheet or large plate. Repeat with all of the truffles. It's ok if the mixture starts to melt a bit while rolling. Once all of the truffles are rolled, place in the refrigerator to chill until firm (20-30 minutes). Once firm, re-roll the truffles to fine tune their round shape and then place in the freezer for an hour.
Line a baking sheet with parchment paper. Heat the bittersweet chocolate in a large heatproof bowl set over a pot of simmering water and stir until smooth. Remove from heat. Place a slotted spoon or spatula over the bowl of chocolate and then place a frozen truffle on top. Use a ladle to pour chocolate over the truffle until covered, allowing the excess chocolate to drip back into the bowl. Place the truffle on the baking sheet and repeat with the remaining truffles. Place the baking sheet in the refrigerator until the chocolate firms up.
I like to begin this recipe a day in advance. Follow steps 1 and 2 in the evening and the remaining steps before serving.