Step 1

Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.

Step 2

Place chicken thighs, leek, carrots, celery, peas, parsley, garlic, shallot, tarragon, salt, basil, pepper, and bay leaves into a large pan. Pour in milk and stir to blend ingredients. Bring to a simmer. Cover and continue to simmer for 15 minutes. Remove from the heat and allow to cool slightly. Strain off milk and set aside in a bowl. Separate chicken and vegetables into two bowls. Tear chicken into rough chunks when cool enough to handle.

Step 3

Melt butter in the same pan over medium heat. Sprinkle in flour, stirring frequently and breaking up any chunks. Continue to stir and cook until thickened and golden, making a roux. Gradually add the strained milk, stirring until you have a sauce. Stir in heavy cream and Dijon mustard, then add the chicken and vegetables. Remove from heat and let cool slightly, about 5 minutes.

Step 4

Pour chicken mixture into the prepared baking dish. Roll out the puff pastry and overlap the pieces to cover the casserole. Glaze the pastry with beaten egg and make several vents in the pastry using a sharp knife.

Step 5

Bake in the preheated oven until golden, 30 to 40 minutes.