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In deep skillet, heat oil on medium heat. Add onion, garlic, celery and carrots and sauté until soft, about 5-10 minutes.
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Add peas, chicken broth and flour and mix until flour is combined and liquid thickens.
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Add milk, salt, pepper and shredded chicken and mix in.
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Preheat oven to 350 degrees F. Grease 18x13-inch sheet pan.
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Pour mixture into sheet pan.
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On flat work surface, roll out each puff pastry. Use pizza cutter to cut into 1-inch strips. Lay strips over filling in lattice pattern.
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Brush pastry strips with egg wash.
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Bake 30-40 minutes until golden brown. Let cool slightly before serving.
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Refrigerate in airtight container 1-2 days, or freeze for later.