1. Cut the chops into chunks and trim off excess fat. Set aside.
2. Render down the fat on a gentle heat in a heavy pan, discarding the pieces.
3. If the carrots are young and the onions small, leave them whole. Otherwise, prepare and cut them into chunks.
4. Toss the meat in the hot fat until it is slightly browned, then quickly toss the vegetables as well.
5. Layer the meat and vegetables in a large oven-proof casserole, carefully seasoning each layer with salt and pepper.
6. Deglaze the pan with the stock or water and pour into the casserole
7. Peel the potatoes and lay them on top of the casserole so that they will steam while the stew cooks. Season the potatoes.
8. Add the sprig of thyme, bring to a boil on top of the stove. Cover and transfer to 375f degree oven, or allow to simmer on top of the stove, until the stew is cooked - about 1 1/2 hours, depending on whether the stew is made with lamb or mutton.
9. When the stew is cooked, pour off the cooking liquid, degrease it and reheat in another saucepan. If you wish, you can thicken it slightly by whisking in a little roux into the boiling liquid. Check seasoning and pour back over the stew.
10. Bring back up to the boiling point, sprinkle with chopped parsley and chives and serve from the pot. Or, for a really appetizing way to present this dish, brown the top layer of the potatoes under the broiler, sprinkle with the herbs, and then serve.