If you have a pressure cooker or instant pot, put the chicken and porcini in it with the water and cook on high for 30 minutes, allowing to depressurise naturally. If you don't, then put them on together to boil with a lid on and cook until the chicken is falling from the bone.
Drain and allow to cool, reserving the broth.
Remove the chicken meat from the bones and reserve.
Take the rehydrated porcini mushrooms and chop finely.
Slice the leek and garlic finely and soften with the butter and a pinch of salt over a low heat until the leek is very soft.
Turn up the heat and add the wine and boil until reduced by half.
Add the reserved broth, meat and mushrooms, add the tarragon and bring to the boil.
Turn off the heat and stir the cream through. Adjust for salt and pepper.