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 five 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.