Heat the oil in a large sauté pan with a lid or fairly deep frying pan. Add the chicken and brown the pieces over a high heat for 3 minutes, stirring constantly. Reduce the heat to medium. Stir in the onion, mushrooms, bay leaf, thyme, tarragon, if using, and lemon zest. Cook for 4 minutes or until the onion and mushrooms are beginning to soften.
Pour in the sherry and boiling water. Add the carrots and salt and pepper to taste, then stir to mix all the ingredients. Bring to the boil, then reduce the heat and cover the pan. Simmer for 5 minutes.
Stir in the broccoli florets. Increase the heat to bring the liquid back to a steady simmer. Cover the pan and cook for 5 minutes or until the pieces of chicken are tender and the vegetables are just cooked. Remove and discard the bay leaf, and the sprigs of thyme and tarragon, if used.
Blend the cornflour to a smooth paste with the cold water. Stir the cornflour paste into the casserole and simmer for about 2 minutes, stirring constantly, until thickened and smooth. Stir in the parsley and serve.