Peel and halve the shallots. Peel and roughly chop the carrot. Trim the celery stick and slice it. Slice the mushrooms, or quarter or halve them if they are small.
Warm a casserole dish or deep frying pan over a medium heat for 2 mins. Add 1 tbsp olive oil and the chicken thighs, skin side down, and and drumsticks. Fry for 5 mins till the skin is golden brown. Turn the thighs and drumsticks over and fry for another 2 mins. Lift the chicken out of the pan and pop them on a plate.
Add the shallots, carrot, celery and mushrooms to the pan. Season with salt and pepper. Cook over a medium-low heat for 5 mins, stirring a few times, till the veg are soft and glossy looking.
While the veg are cooking, peel and roughly chop the potato. Peel and crush the garlic. Finely chop the parsley stalks and set the leaves to one side. Crumble the stock cube into a measuring jug and stir in 450ml boiling water.
Stir the potato, garlic and parsley stalks into the veg with the Dijon mustard. Add the bouquet garni. Pop the chicken back in to the pan. Pour in the stock. Cover and turn up the heat. Bring the casserole to the boil, then turn the heat back down and simmer for 30 mins.
The chicken should be cooked through and the veg tender. Turn off the heat. Lift out the bouquet garni and discard it. Stir in 4 tbsp double cream.
Taste the casserole and add more salt and pepper if you think it needs it. Ladle the chicken casserole into 2 warm bowls, scatter over the parsley leaves and serve.