Place the softened butter in a bowl and stir in the mustard, honey and finely chopped tarragon, season with sea salt and freshly ground black pepper and mix well. Rub 2/3 of the tarragon and mustard butter all over the chicken and between the skin and breast meat.
Melt the remaining tarragon and mustard butter in a small saucepan over a medium heat, once melted remove from the heat. Place the parsnips in a bowl and pour the melted butter on top and toss to coat.
Place the buttered parsnips on to a baking sheet along with the three sprigs of fresh tarragon and place the whole chicken on top. Transfer to the pre-heated oven and roast for one hour and 20 minutes. Baste the chicken and parsnips half way through cooking.
Once the chicken is cooked, remove from the oven and use aluminum foil to tent the chicken (to keep it warm). Allow to rest for ten minutes before you slice and serve.