Chop candies in food processor until crushed but not ground. With electric mixer, beat 1 1/2 cups cream, 1/4 cup sugar, vanilla, and peppermint extract in large bowl until soft peaks form. Fold crushed candy into peppermint cream.
Spread 1 tablespoon peppermint cream on chocolate wafer. Top with another wafer and repeat 4 more times to produce stack of 6 wafers with cream in between each cookie. Make 6 stacks, each with 6 wafers. Spread 1 tablespoon peppermint cream on top of 5 stacks, leaving 1 stack plain.
Place cookie stacks on sides and put them together end to end, making one 16-inch log. A plain stack without cream on top wafer should be placed at end. Wrap log in plastic and freeze until firm, at least 5 hours.
With electric mixer, beat remaining cream, remaining sugar, and cocoa in large bowl until stiff peaks form.
Cut thin piece diagonally from one end of frozen log and discard. Cut 2-inch piece diagonally from other end of frozen log and set aside.
Transfer frozen cake to serving platter and spread all but 1/2 cup cocoa cream evenly over the log. Press reserved 2-inch piece on top of log to make bump, placing it several inches from one end of log. Cover bump with remaining cocoa cream.
Drag tines of fork down length of log to simulate bark.
Freeze until firm, at least 3 hours.
Let stand at room temperature for 20 minutes before serving.