Bring first 4 ingredients to a boil in a Dutch oven. Cover, reduce heat, and simmer 1 hour or until tender.
Remove chicken, reserving 3/4 cup broth; discard onion and bay leaves. Cool, skin, bone, and coarsely chop chicken, set aside.
Whisk together all-purpose flour and vegetable oil in Dutch oven; cook over medium heat, whisking constantly, 15 to 20 minutes or until roux is caramel colored. Stir in chopped bell pepper, onion, and garlic; cook 2 minutes. Add sliced okra, tomatoes and chiles, dried thyme and reserved 3/4 cup chicken broth. Cover, reduce heat, and simmer 30 minutes.
Peel shrimp, and devein, if desired. Add shrimp and 2 cups chopped chicken to gumbo; cook 8 minutes or just until shrimp turn pink. Remove from heat, and cool slightly.
Roll out pastry sheet on a floured surface; cut into 4 (5-inch) squares. Return pastry to freezer for at least 15 minutes. Cut out decoratives shapes from excess pastry strips.
Ladle gumbo into 4 ovenproof soup bowls, filling three-fourths full. Place 1 pastry square over each bowl, pressing firmly to sides to seal edges. Place decorative shapes on top of pastry. Brush pastry with egg.
Bake at 400º for 20 minutes or until pastry is puffed and golden. Serve pot pies with hot sauce, if desired.