Rinse the poussin and pat dry with kitchen paper. Season all over with salt and pepper. Melt half the butter with the oil in a large flameproof casserole and fry the walnuts for a couple of minutes until beginning to colour. Lift out with a slotted spoon on to a plate. Add the courgettes to the casserole and fry for about 5 minutes until lightly browned on both sides. Lift out on to the plate and set aside.
Melt the remaining butter in the casserole and fry the onion for 2 minutes. Add the poussin and fry for 5 minutes until golden on all sides. Add the garlic and stock and bring to the boil. Cover with a lid or foil and cook in a preheated oven, 180°C (350°F), Gas Mark 4, for 45 minutes. Add the tarragon leaves to the casserole with the walnuts and courgettes, then return to the oven for a further 30 minutes.
Lift the poussin from the pan on to warmed serving plates. Drain the walnuts and courgettes on to the plates with a slotted spoon. Stir the soured cream into the sauce and bring to the boil. Check the seasoning, then spoon on to the plates. Serve with grainy bread or creamy mash, if liked.