In a large dutch oven, combine olive oil, carrots, celery, onion, garlic and thyme over medium-high heat. Season generously with salt and pepper. Cook until onion and celery have become translucent.
Add flour to mixture and stir to combine. Stir in chicken broth and cream, then bring mixture to a simmer.
Add chicken and peas to mixture. Continue to cook until sauce has thickened. Season to taste with salt and pepper.
Roll out thawed puff pastry dough on a lightly floured surface. Slice dough into 2 inch X 4 inch strips and transfer to a parchment paper lined baking sheet.
Brush dough with egg wash and season top with thyme and salt.
Bake puff pastry for 15 minutes or until top is golden brown and pastry is crispy. Serve with chicken mixture and enjoy!