Start by placing the dried porcini in a bowl and covering them with 250ml of just-boiled water. Let them soak for about 30 minutes while you slice the leeks and peel and cube the celeriac. This soaking step is what gives the filling its deep, savory flavor later on.
Heat the olive oil in a large saucepan and add the leeks, celeriac and salt. Cook for about 10 minutes until the leeks soften, then stir in the garlic, chestnut mushrooms and chopped porcini. Pour in the reserved porcini broth, cover, and simmer until the celeriac turns soft.
Stir the pepper, mustard and cheddar into the filling until melted, then fold in the cream and tarragon. Tip everything into your pie dish, top with the puff pastry, brush with egg, and cut a few slits for steam. Bake until the pastry turns golden and puffed.