Push the tarragon into the chicken and place in a large stockpot with the carrots, celery, bay leaf, parsley stalks, and onion. Cover with 8 to 12 cups of water, bring to a boil, then simmer gently for 1 hour until the vegetables are tender. Transfer the chicken to a plate and cool slightly. Strip the meat from the chicken and separate into evenly sized pieces. Divide the meat between 4 small pie dishes. Strain the stock into a clean pot, discarding the vegetables and herbs. Bring to a boil and simmer until reduced by half.

Put the porcini in a bowl, pour over 1 cup of boiling water, soak for 20 minutes, then drain, reserving the liquid. Chop the porcini finely. Strain the reserved liquid through coffee filter paper set over a measuring cup. Add stock to make 2-3/4 cups, reserving remaining stock for another use.

Melt the butter in a skillet, add the onions and porcini, and cook gently for about 3 minutes. Add the pancetta or bacon and cook for 2 to 3 minutes to soften the onion and lightly color the bacon. Add the flour and cook without browning for 1 to 2 minutes. Gradually add the stock, stirring until thick and smooth. Add the lemon juice, cream, and tarragon, bring to a boil, season to taste, then remove from the heat. Let cool slightly, then portion into the pie dishes.

To make the pastry, sift the flour and salt into a bowl, then rub in the butter until the mixture resembles fine crumbs. Mix in the potato to form a soft but firm dough. Roll out to 1/4-inch thick then cut 4 rounds slightly larger than the pie dishes. Brush the edges of the dishes with water then cover with a pastry lid. Trim the edges, roll out any excess pastry, and use to decorate. Make a small steam hole in the center of each pie and brush the tops with beaten egg yolk. Bake in a preheated oven at 400°F for 15 minutes, reduce heat to 350°F and bake for a further 15 to 20 minutes or until the pastry is crisp and golden brown.