To make the crust, place the graham cracker sheets in a large resealable plastic bag and seal the bag. Using the bottom of a mixing bowl, a rolling pin, or your hands, crush the graham crackers into fine crumbs. Melt the butter in a medium bowl in the microwave, and then allow to cool for 1 to 2 minutes. Add the graham cracker crumbs to the melted butter and stir to combine. Pour the mixture into an 8 x 8-inch baking dish and spread it evenly over the bottom, pressing it gently into the corners. Bake until the crust is lightly browned, about 10 minutes. Remove the baking dish from the oven and set it aside to cool for about 10 minutes.
Meanwhile, mash the bananas in a small bowl. In a medium bowl, stir together the peanut butter, yogurt, and vanilla extract until combined. Add the mashed bananas and fold gently until thoroughly incorporated. Spoon the banana mixture over the cooled graham cracker crust. Place the baking dish in the freezer and chill until completely frozen, at least 3 hours.
Before serving, melt the chocolate in a small bowl in the microwave, about 1 minute, stirring halfway though. Remove the baking dish from the freezer and drizzle the melted chocolate over the top. Slice into 2 x 2-inch pieces and serve.