Heat the oil in a saucepan, add the chicken and onion and fry for 5 minutes, stirring until browned. Stir in the flour, then gradually mix in the stock. Bring to the boil, then add the mustard, carrot and a little seasoning. Cover and simmer for 30 minutes.
Meanwhile, cook the potatoes in a saucepan of boiling water until tender. Add the courgettes, sugar snap peas and frozen peas to a smaller saucepan of boiling water and cook for 3 minutes. Drain and set aside.
Drain the potatoes and mash with two-thirds of the butter and all the milk. Season and stir in two-thirds of the cheese.
Spoon the chicken mixture into a 1.3 litre (2¼ pint) pie dish or 4 individual dishes, add the just-cooked green vegetables, then spoon the mash on top. Dot with the remaining butter and sprinkle with the remaining cheese. Grill until golden, then serve immediately. (For an oven-baked chicken thatch, chill the dish once the grated cheese has been sprinkled on top, then bake when needed, in a preheated oven, 190°C (375°F), Gas Mark 5, for 35 minutes until piping hot or 25 minutes for smaller dishes.)