Preheat oven to 400ºF. Line a large baking sheet with parchment paper or foil.
On a lightly floured countertop, roll each piece of dough into a 6-by-10-inch rectangle. With a floured chef's knife, cut each rectangle into six 10-inch strips. Make 3-inch lengthwise cuts at one end of each strip, 1/4 inch apart, to form broom straws. Twist and pull uncut portion of strips to form a broom handle (each breadstick will be about 15 inches long). Gently transfer broomsticks to prepared baking sheet; place at least 2 inches apart. Separate cut ends.
Brush broomsticks with milk and sprinkle with Parmesan. Bake until golden, 15 to 18 minutes. Serve warm or at room temperature.
In addition to using parm cheese as a topping I also made some with course salt and some with both salt and cracked pepper. My brooms came out looking more like chicken feet so I added some fingers and other bones and presented it as a pile of bones on a plate instead of broomsticks. I used tin foil and was surprised they didn't stick. I would make this again.
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