Preheat the oven to 400 degrees F. Line a sheet pan with parchment or buttered waxed paper.
Unroll the puff pastry on a work surface. Brush the pastry generously with melted butter.
In a small bowl, toss together the sugar and cinnamon. Sprinkle evenly over the pastry.
Working lengthwise, cut the pastry in half and then cut each half into 6 even strips, each 3/4-inch wide. Twist the strips to make long twisted "straws".
Transfer to the prepared pan, pushing the ends down with your thumb to help them stay in place on the pan and remain twisted. Bake until puffed and golden brown, about 20 minutes.
To make the sauce, heat the milk in a saucepan. Pour the hot milk over the chocolate and whisk to melt it. Whisk in the peanut butter until smooth. Keep sauce warm until ready to serve.
To serve, place the twists on a tray and serve with the sauce along side for dipping.