Cook the chicken and make the broth: may be prepared 1 day in advance
1. Wash the chicken under cold, running water and pat dry with paper towels. Put the chicken into a large pot, cover with cold water and bring to a boil over medium-high heat. Reduce to a simmer and cook for 15 minutes, carefully skimming off any impurities that accumulate on the surface.
2. Season with salt and pepper, add the bouquet garni seasoning packet, onion, carrots and celery. When the water returns to the boil, reduce to a persistent simmer and cook, uncovered, for 45 minutes.
3. When the chicken is thoroughly cooked remove from the broth and cool. As the chicken cools, strain the broth from the chicken, and reserving the broth, discard the vegetable solids. When the chicken is thoroughly cold, strip off and discard the skin. Strip the meat from the bones, and shred using scrupulously clean hands and an immaculate work station. (If you wish you may now refrigerate the chicken and cooled broth for up to 48 hours.)
Pre-heat the oven to 375°F. Bake the pastry tops
4. Use a pastry cutter, dividing the cold puff pastry into 3-inch circles. Cover a cookie sheet with baker’s paper, place the rounds on the paper, and bake in the preheated oven for 5 minutes or until they are nicely browned. Remove the pastry and keep warm.
Make the pot pie filling and finish:
5. Heat the olive oil in a large pot or casserole over medium heat, add the shallots and sauté them. After 3 minutes, add the mushrooms, raise the heat, and cook for 5 minutes. Season with salt and pepper. Add the butter to the mushrooms, allow to heat and bubble before adding the flour to make a quick roux to thicken the sauce. Add warm chicken broth, stirring in with a whisk; add the cream and bring the liquid to a boil, cook for 10 minutes. To the pot with the mushrooms, chicken broth and cream, add the chicken meat. Bring to a boil, lower the heat and simmer for 20 minutes. Add the tarragon leaves, and transfer to small ovenproof dishes or crocks (soufflé dishes will do), top each with a pastry lid and serve at once.