For the casserole, preheat the oven to 180C/160C Fan/Gas 5.
Heat 1 tablespoon of the oil in a heavy-based casserole over a medium heat. Add the carrots and celery and fry for 4-5 minutes, or until lightly browned.
Add the chicken bones (if using; omit if cooking a vegetarian version of this dish) and fry for a further 2-3 minutes, stirring well.
Add the garlic bulb, tomatoes, thyme and parsley stalks and stir again.
Pour in 1.2 litres/2 pints water and bring the mixture to the boil. Reduce the heat then simmer for 25 minutes. Strain the resulting stock through a fine sieve, collecting the liquid in a clean saucepan. Simmer until its volume has reduced by about one-third. Keep warm.
Meanwhile, heat another tablespoon of the oil in a frying pan over a medium heat. Add the onion and fry for 4-5 minutes, or until softened and lightly browned. Stir in the coriander, then season, to taste, with salt and freshly ground black pepper. Remove from the pan and set aside.
Add another tablespoon of the oil to the frying pan, then fry the peppers until just softened (about 3-4 minutes). Season, to taste, with salt and freshly ground black pepper.
Spoon half of the onion mixture into the bottom of a pie dish. Top with half of the peppers, then cover with a layer of the sliced roast potatoes, keeping the best shaped slices for the top layer.
Repeat the layering process with the remaining onions and peppers, then pour enough of the warm stock into the pie dish to just cover the top layer of peppers.
Decorate the top of the casserole with a layer of the remaining potato slices. Brush the potato slices all over with a mixture of the melted butter and the remaining tablespoon of oil.
Cook the casserole in the oven for 20-30 minutes, or until the potatoes are crisp and golden-brown and the casserole is bubbling.
Meanwhile, for the mushrooms, heat the oil and butter in a large frying pan over a medium heat. Add the garlic and fry for 1-2 minutes, or until softened.
Add the mushrooms and fry for 2-3 minutes, or until softened and just coloured. Stir in the coriander just before serving.
To serve, spoon the red-pepper-and-onion casserole onto serving plates. Serve the garlic-and-coriander mushrooms alongside, with any remaining warm roast potato slices.