Melt the chocolate in a double boiler over medium heat, or in the microwave on 50% power, until nearly melted. Remove from heat and stir until smooth. Using a pastry brush, brush one side of each matzo piece with the melted chocolate. Sprinkle 8 with the chopped pistachios. Let stand to harden.
In a medium bowl mash the blackberries. Gently fold the berries into the whipped topping. Do not over mix; leave streaky. Divide the blackberry mixture between 8 of the chocolate-covered matzo (without pistachios). Sandwich with the remaining matzo. Serve immediately.