1. Preheat your oven to 400°F (200°C). This ensures a beautifully golden crust.
2. In a large skillet, heat olive oil over medium heat. Add the diced onion and garlic, sautéing until fragrant and translucent, about 3-4 minutes.
3. Add the carrots and celery, cooking until they begin to soften, another 5 minutes.
4. Sprinkle the flour over the vegetables, stirring to coat evenly. Cook for an additional 2 minutes to eliminate the raw flour taste.
5. Gradually whisk in the chicken broth and milk, stirring constantly until the mixture thickens, about 5 minutes.
6. Stir in the cooked chicken, peas, salt, pepper, thyme, and paprika. Let the filling simmer for 5 minutes, allowing the flavors to meld together.
7. Transfer the filling into a pie dish. Carefully lay the puff pastry over the top, trimming any excess and crimping the edges to seal.
8. Brush the pastry with the beaten egg for a glossy finish. Cut a few slits in the top to allow steam to escape.
9. Bake for 25-30 minutes, or until the crust is golden brown and the filling is bubbling.

This recipe is a true family favorite, a testament to the power of a home-cooked meal. As my grandmother would say, “Cocina con amor y todo saldrá bien” — cook with love, and everything will turn out fine.