If your puff pastry sheet is still frozen, pull it out to thaw before you start the chicken and vegetables.
Heat a bit of oil over medium heat in a large skillet and add the chicken pieces, cooking and stirring until cooked through, about ten minutes but it depends on how large your pieces are and how hot your pan is. When you can easily cut a piece in half with a wood spatula, they're done! Remove the chicken pieces to a 9x9 baking dish (or similar) but leave as much oil in the pan as you can.
Add the leeks and onion and carrot and cook a few minutes, stirring. Add more oil if the pan looks too dry.
Add the quartered mushrooms and cook, stirring, another few minutes.
Sprinkle the flour over the vegetables and cook another 4-5 minutes, stirring.
Stir in the broth and water or beer and bring to a simmer. Add the chicken pieces back into the pan. Lower the heat to just keep the liquid simmering and add the tarragon, parsley and bay leaf. Add salt and pepper to taste.
Turn the oven to 350 to preheat.
Simmer the chicken mixture about 10-15 minutes, until thickened. Taste and adjust seasoning.
Pour the chicken and vegetable mixture into a 9x9 pan or something similar.
Top the chicken mixture with the puff pastry, cutting it as needed to cover your pan. Cut some slits in the top to let the steam escape.
Bake about 30 minutes. Let cool a few minutes before serving.