Before assembling, stir the chocolate pudding to soften it. In a 11 x 8-inch (28 x 20 cm) serving dish, spread half of the pudding. Cover with a third of the cookies, overlapping them slightly. Break the cookies, if needed. Top with the remaining pudding. Cover with another third of the cookies. Layer with the banana compote (if needed, whisk to soften before spreading) and half of the whipped cream. Cover with the remaining cookies and top with the remaining whipped cream.