For the chicken, season the chicken with salt and black pepper. Heat a large frying pan or sauté pan until hot. Add the oil and half the butter. Fry the chicken skin-side down for 1-2 minutes, or until golden-brown.
Turn and fry on the other side for another 1-2 minutes, then remove from the pan.
Add the remaining butter, the pancetta, carrot, mushrooms, shallots and garlic, and fry until golden-brown.
Add the wine and bring to a simmer, stirring to deglaze the pan.
Put the chicken back into the pan with the tomato purée and tarragon and bring to a boil.
Reduce the heat to a simmer and cook for 30-40 minutes until the chicken is tender and the liquid slightly reduced in volume.
Add the tomatoes, flatleaf parsley and season to taste with salt and pepper.
Simmer for a further two minutes.
For the mash, place the potatoes into a pan of cold, salted water and bring to the boil.
Reduce the heat and simmer for 12-15 minutes, or until the potatoes are tender.
Drain and return to the pan, then place over a low heat for one minute to dry the potatoes slightly.
Mash thoroughly, then add the butter and milk and beat to form a smooth mash.
Season to taste with salt and black pepper.
Serve each person two pieces of chicken with the sauce spooned over and a dollop of mash.