Step 1

Preheat the oven to 400°F/200°C. Arrange chicken pieces on a rimmed baking sheet and season with salt and pepper. Roast for about 15 to 25 minutes (SEE NOTE BELOW), or until the internal temperature reaches 165°F/75°C when checked with an instant read thermometer. Cool the chicken enough to handle, then shred and set aside.

Step 2

In a medium pot over medium heat, melt the butter. Add the leeks, thyme, and a big pinch of salt and cook until tender, about 10 minutes. Stir in the flour and cook for about 1 minute. Gradually stir in the chicken broth, cream, and mustard until smooth, and bring to a simmer, stirring frequently. Cook until thick, about 5 minutes. Taste and season with salt and pepper, then stir in the shredded chicken. Set aside to cool to room temperature before assembling, about 30 minutes.

Step 3

Transfer filling to a greased 1 ½ to 1 ¾ quart baking dish (such as 10 ½-by-7-inches rectangular or 8-to-8 ½ inches square). Unroll or unfold your thawed puff pastry sheet. If it’s not already the right size or dimensions, on a lightly floured work surface roll out the puff pastry into a rectangle or square just larger than your baking dish. Brush the edge of the dish with water. Lay the pastry over the baking dish and gently press the edges to seal to the baking dish. Fold over any excess dough to create a tall border. Use the tines of a fork to crimp the edges.

Step 4

Lightly brush beaten egg over the top of the pastry, then use a sharp knife to cut 3 slits as vents. Transfer the pie to a rimmed baking sheet (in case of drips) and bake at 400°F/200°C until the puff pastry is dark golden brown all over and the filling is bubbly, about 50 to 60 minutes. If the edges brown too quickly for your liking, you may carefully tent some aluminum foil over them partway through baking.