In a large bowl, whip 1 1/2 cups cream with sugar until soft peaks form. In a small bowl, whisk peanut butter until soft and smooth; whisk in 1/2 cup cream until light and fluffy. Fold peanut-butter mixture into whipped cream until incorporated.
Dab the bottom of 6 cookies with a very small amount of cream mixture and arrange in a circle on a serving plate; place 1 cookie in the middle of circle. Top with cup cream mixture, spreading outward to cover all but outer edges of cookies. Repeat process 5 more times (staggering the cookie layers), ending with cream. Cut 3 cookies in half; decorate top of cake with cookie halves.
Refrigerate cake at least 8 hours (or up to overnight). To serve, cut into wedges with a serrated knife.
To achieve a cakelike texture, let the dessert stand for at least 8 hours before serving.