Preheat the oven at 180°C
Separate the tarragon leaves from the branches and chop the leaves finely. Keep the branches. In an oven proof, heavy based pan, melt the butter and oil until it starts foaming. Add the chicken pieces and sauté until they are golden brown all over. Add the brandy and flambé. Remove the chicken from the pan and keep aside.
Add the shallots, stir for 1 minute and add the tarragon branches and the wine. Add a good pinch of salt and cracked pepper and return the chicken to the pan. Cover with the lid and bake for 35 minutes or until the meat can detach easily from the bone. Remove the chicken pieces from the pan and place onto a serving dish. Keep warm.
Place the pan on high heat, add half of the tarragon leaves and bring to the boil and let it reduce for a few minutes. Mix the egg yolks with the cream until smooth. Remove pan from heat and stir in the egg mixture. The sauce should be smooth and not too thick.
Pour the sauce over the chicken and sprinkle the rest of the tarragon leave over the meat.