Put the stock into a wide-based pan and boil it vigorously until it has reduced to 175ml/6fl oz.
Season the chicken breasts on both sides with salt and pepper.
Heat a small knob of the butter in a large frying pan and, when it is foaming, add the chicken breasts, skin-side down, and cook over a medium heat for six minutes until the skin is crisp and richly golden. Turn the chicken breasts over and continue to cook them for 6-7 minutes until cooked through.
Thinly slice the black pudding into 16 or so slices. Remove the chicken from the pan and keep warm. Add the slices of black pudding to the pan and fry them for one minute on each side. Set them aside with the chicken.
Add the sweet wine to the pan and boil, scraping up all the browned bits from the bottom of the pan with a wooden spoon, until reduced to about three tablespoons. Add the reduced chicken stock and boil for 1-2 minutes. Whisk in the rest of the butter a small piece at a time, then add the lemon juice and some seasoning to taste.
Drop the spinach, a large handful at a time, into a large hot pan, adding another as each one wilts down. When all the spinach has been added, cook for one minute, tip into a colander and lightly press out the excess liquid.
Melt the butter in the pan, add the spinach, and season with freshly grated nutmeg and some salt and pepper. Toss briefly over a high heat to combine.
To serve, slice the chicken breasts diagonally and at a slight angle and arrange the slices in the centre of each warmed plate with the black pudding.
Stir the tarragon leaves into the sauce and spoon some of it over the chicken and a little around the outside edge of the plates. Serve with the steamed spinach.