Working on a lightly floured surface, stack 2 pieces of thawed puff pastry on top of each other. Roll dough into a 13”x13” square. Using a pizza wheel, cut the dough into (13) 1” strips.
Place puff pastry in refrigerator until needed.
Preheat oven to 400°F.
Spray a 13”x18” rimmed baking pan with nonstick baking spray; set pan aside.
Using a large, deep skillet (or pot), add butter and place over medium heat. Once butter has melted, add onions; sauté for 5-6 minutes, stirring occasionally, or until onions are translucent.
Add flour, salt, ground cumin, smoked paprika and pepper to skillet; stir until well combined.
Add chicken broth and milk; stir until well combined. Continue cooking over medium heat, stirring often, for 4-5 minutes or until mixture has thickened noticeably.
Meanwhile, using a large bowl, combine the chicken, carrots, celery, peas and corn. Spread mixture evenly onto prepared sheet pan.
Pour chicken broth mixture evenly on top of the of the sheet pan.
Remove puff pastry strips from refrigerator and lay strips crosswise on top of the filling.
Brush the top of the pastry strips with the beaten egg.
Bake for 35-40 minutes, or until puff pastry turns golden brown in color.
Let cool for 10-15 minutes and then serve with a flat spatula.