Cook the vegetables

• Melt the butter in a skillet over medium heat.
• Add the onion, carrots and celery and cook until softened.
• Stir in the garlic and thyme and cook until fragrant.

Make the creamy filling

• Sprinkle the flour over the vegetables and stir to coat.
• Pour in the chicken broth and heavy cream, stirring until smooth.
• Simmer until the sauce thickens, then season with salt and pepper.

Add chicken and peas

• Stir the shredded chicken and frozen peas into the sauce.
• Cook until everything is heated through.

Assemble the pie

• Pour the filling into a baking dish.
• Lay the puff pastry over the top and press the edges to seal.
• Brush the pastry with the beaten egg and cut a few slits for steam.

Bake

• Bake at 200 °C until the pastry is puffed and golden brown.
• Let rest a few minutes before serving.