Preheat oven to 400°F with rack in lower third position. If using Jus-Rol, preheat to 425 and place rack in middle position. On a lightly floured surface, roll puff pastry into a 10-inch square. Cut 2 to 3 (2-inch) slits horizontally across the center of pastry, spacing each 1-inch apart.  Place on a large plate or small baking sheet, chill in fridge while you make the filling.

Melt butter in a deep 10-inch ovenproof skillet over medium.  (I used a cast iron skillet.) Add shallots and garlic; cook, stirring often, until softened, about 2 minutes. Stir in wine and bring to a boil over medium; cook until reduced by half, about 2 minutes, stirring occasionally. Whisk together flour, Dijon mustard and chicken broth in a measuring cup; stir into skillet and cook, whisking constantly, until mixture thickens, 1 to 2 minutes. Stir in chicken, lemon juice, dill, parsley, tarragon, veggies and 1 teaspoon salt, and 1/4 teaspoon pepper. Remove from heat.

Whisk together egg and water in a small bowl. Place pastry square over hot chicken mixture, letting ends extend over sides of skillet. Brush pastry evenly with egg wash. Sprinkle with remaining 1/8 teaspoon each salt and pepper. Brush the undersides of the puff pastry corners with the egg wash; press to the skillet. Place skillet on a rimmed baking sheet.

Bake until top is browned and filling is bubbly, about 20 minutes. Mine took a bit longer. Remove from oven and let stand 10 minutes. Sprinkle with fresh parsley and serve.