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Preheat oven to 400 F.
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Melt butter in a large saucepan over medium-high heat.
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Add celery, carrots, onion and potatoes. Sauté for 8 to 10 minutes, or until vegetables begin to soften.
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Add garlic and season with salt and pepper.
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Mix in flour, chicken broth and cream cheese. Let cook for 5 minutes more, stirring constantly.
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Fold in chicken and peas.
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Pour mixture into a baking sheet sprayed with nonstick cooking spray.
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Roll out 2 puff pastry sheet to the width of the sheet pan, cut into 1 inch strips and lay over filling.
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Use a sharp knife to cut off any excess dough hanging over the sides.
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Whisk egg in a small bowl and brush the tops of the puff pastry strips.
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Cook for 30 to 35 minutes, or until top is golden brown.
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Remove from oven, garnish with parsley and serve.