Line an 8- or 9- inch square baking pan with foil.
Melt 8 tablespoons of the butter and add to a large bowl. Add the graham cracker crumbs, sugar, vanilla and 1 cup of peanut butter and stir until well combined. Transfer the peanut butter mixture to the prepared baking pan and smooth with an offset spatula to create an even layer.
Combine the chocolate chips, the remaining 4 tablespoons butter and the remaining tablespoon peanut butter in a medium microwave-safe bowl and microwave in 30-second intervals, stirring after each, until melted. Alternatively, this can be done over a double boiler. Pour the chocolate mixture over the peanut butter and smooth with an offset spatula. Arrange the pretzel sticks on the surface of the chocolate, pressing them lightly to adhere. Refrigerate until hardened, about 1 1/2 hours. Cut into squares to serve.