In a large pot, bring broth to a boil over high heat. Add potatoes, carrots, and green beans. Cover and bring to simmering; then reduce heat and cook until carrots are tender to bite, about 5 minutes. Drain, reserving broth, and set vegetables aside.
Melt butter in pot over medium-high heat. Add onion, mushrooms, celery, thyme, rosemary, pepper, and salt. Sauté until vegetables are soft, 7 to 10 minutes. Reduce heat to medium. Add flour and cook, stirring, until light golden, about 3 minutes. Whisk in milk until blended, then add reserved broth and whisk until no lumps remain. Cook, whisking, until simmering, 10 to 12 minutes.
Remove sauce from heat and stir in reserved vegetables and the chicken. Pour into a shallow baking dish about 9 by 13 in. Let cool to room temperature, about 30 minutes.
Meanwhile, preheat oven to 375°. On a lightly floured work surface, roll 1 pastry sheet into a rectangle 1 in. longer and wider than baking dish. With a small knife, score a 1/2-in. border on all sides of pastry without cutting through it. Slide pastry onto a baking sheet and chill. Re-flour work surface and roll second pastry sheet to a 10- by 12-in. rectangle. Cut out 3 skulls, using a 5- by 3 1/2-in. skull-shaped cookie cutter.* Cut 4 each of large and medium bones, using 4- by 1 1/2-in. and 3 1/2- by 1 1/2-in. bone-shaped cookie cutters. Using a knife tip, score faces in skulls without cutting through pastry. Transfer skulls and bones to a baking sheet and chill until cold.
Set chilled pastry rectangle onto cool chicken mixture, gently pushing it along score lines into edges of dish. Brush with egg. Arrange large bones on pastry and brush with egg; then arrange skulls and medium bones on top, overlapping a bit if needed, and brush with egg.
Bake until pastry is well browned, about 40 minutes; if filling starts to bubble over, put a baking sheet on lower rack under pot pie.
*We used a skull cookie cutter and dog-bone cookie cutter set from CopperGifts.com.
Make ahead: Through step 4, up to 1 day, filling and pastry chilled separately airtight. To continue with step 5, bring filling to room temperature, 2 hours.