Step 1

Combine broth, miso, pepper, salt, thyme and bay leaves in a large saucepan. Bring to a boil over high heat. Cook, undisturbed, until reduced to about 4 cups, about 10 minutes. Discard thyme and bay leaves.

Step 2

Whisk milk and flour in a small bowl, then whisk into the broth in the pan. Bring to a boil over high heat; cook, stirring occasionally, for 1 minute. Stir in chicken. Remove from heat and let stand for 5 minutes. Stir in mixed vegetables, onions and parsley. Pour the mixture onto a large rimmed baking sheet.

Step 3

Preheat oven to 425 degrees F.

Step 4

Unroll pie crusts on a lightly floured work surface, placing one on top of the other. Roll out into a 14-by-19-inch rectangle. Cut into 2-by-19-inch strips using a decorative wheel or pizza cutter. Place half the strips diagonally across the chicken mixture, leaving 2-inch gaps in between. Weave in the remaining strips to form a lattice pattern. Trim excess dough from the edges and discard. Brush the top of the dough with egg. Sprinkle with pepper to taste.

Step 5

Bake until the top is browned and the chicken is cooked through, 30 to 35 minutes. Let cool for 5 minutes. Cut into 8 pieces.