1) Soak the dried porcini mushrooms in the 240ml of hot water until soft, around 15 minutes. Cook the penne according to the directions on the package.
2) While the penne is cooking, heat the oil in large frying pan over a medium-high heat. Add the leeks and cook for 2 minutes, or until soft. Add the shiitake mushrooms and cook for 3 minutes, until the mushrooms soften.
3) Strain the porcini mushrooms through a sieve, reserving the soaking liquid. Chop the mushrooms and add to the pan. Add the chicken and tarragon and cook for 1 minute, until the tarragon is fragrant.
4) Add the reserved mushroom soaking liquid and 240ml of the chicken stock, bring to a simmer and simmer for 5 minutes.
5) In a small bowl dissolve the cornflour in the remaining 60ml of chicken stock using a whisk, and add to the pan along with the peas. Simmer for 2 minutes until it reaches a full boil, and the sauce thickens.
6) Stir in the cooked penne and cook for 1 minute to heat through. Remove from the heat and stir in the parsley. Season, to taste, with salt and freshly ground black pepper.