Preheat oven to 375 degrees F.
In a large pot, melt butter over medium heat. Add bell pepper, onion, and celery. Cook 5 to 6 minutes until softened.
Add chicken broth and bring to a boil. Remove from heat and stir in stuffing mix until evenly moistened. Set aside.
In a large bowl, combine shredded chicken, cream of mushroom soup, milk, and gravy. Mix until combined.
Butter a 9x13 baking dish. Spread chicken mixture evenly in the bottom. Spoon stuffing over the top, pressing gently to create a flat, even surface. Leave about 1/2 inch of headspace.
On a lightly floured surface, roll each pie crust into a rectangle about 10x14 inches. Cut each into ten 1-inch-wide strips (20 strips total). If dough is soft, refrigerate strips 10 minutes before weaving.
Lay 10 strips vertically across the dish, evenly spaced. Weave remaining strips horizontally in an over-under pattern. Trim or tuck ends just inside the dish rim.
Brush lattice with egg wash. Sprinkle with salt, pepper, or thyme if desired. Place dish on a baking sheet.
Bake 40 to 45 minutes until crust is deep golden and filling bubbles through the lattice. Tent with foil after 30 minutes if browning too fast.
Rest 10 minutes before serving. Serve warm with extra gravy if desired.