How to Make It
Preheat the oven to 400°. On a rimmed baking sheet, season the chicken legs with salt and pepper and drizzle with the olive oil. Roast the chicken for about 30 minutes, until browned and cooked through. Let stand until cool enough to handle. Shred the chicken, discarding the skin and bones. Reserve the pan drippings. Reduce the oven temperature to 375°.
In a large saucepan, melt the butter. Add the onion and leek and cook over moderate heat until tender, about 5 minutes. Stir in the mustard and the flour and cook until pasty, about 1 minute. Whisk in the chicken broth, 3/4 cup of the milk, the heavy cream and the chicken pan drippings and bring to a simmer. Cook over moderate heat, stirring frequently, until thick, about 5 minutes. Stir in the shredded chicken and the tarragon and season with salt and pepper. Let stand until cool, about 30 minutes.
Spread the chicken filling in an 8-by-11 1/2-inch baking dish. On a lightly floured work surface, roll out the puff pastry to a 9-by-13-inch rectangle. Lay the pastry over the baking dish and gently tuck in the overhanging pastry. Using a sharp knife, cut 3 slits in the top of the pastry. In a small bowl, beat the egg with the remaining 1 tablespoon of milk. Brush the egg wash over the pastry and sprinkle with the sesame seeds. Set the pie on a rimmed baking sheet and bake for about 1 hour, until the puff pastry is golden brown and the filling is bubbly. Let stand for 30 minutes before serving.