Sauté the Aromatics

• In a large skillet, heat the olive oil over medium heat. Add the diced onion and cook until translucent, about 4-5 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.

Prepare the Filling

• Add the sliced mushrooms to the skillet and cook until softened, about 5-7 minutes. Stir in the shredded chicken and mix well.

Make the Creamy Sauce

• In a separate saucepan, melt the butter over medium heat. Whisk in the flour and cook for 2 minutes. Gradually add the chicken broth, whisking until smooth. Pour in the heavy cream and bring to a simmer, cooking until thickened. Stir in the dried thyme, tarragon, salt, and pepper.

Combine and Cool the Filling

• Pour the creamy sauce over the chicken and mushroom mixture, stirring to combine. Remove from heat and let cool for 10-15 minutes.

Prepare the Puff Pastry

• Preheat your oven to 400°F (200°C). Roll out the puff pastry on a lightly floured surface to fit your baking dish. Cut slits in the pastry for steam to escape.

Assemble the Pie

• Pour the filling into a greased baking dish and cover with the puff pastry, pressing down the edges to seal. Brush the top with the beaten egg for a golden finish.

Bake the Pie

• Bake in the preheated oven for 25-30 minutes, or until the pastry is golden brown and puffed up. Allow to cool for a few minutes before serving.