Preheat oven to 350 degrees if you plan to finish cooking the stew in the oven.
Cut the lamb steaks in half and trim off some excess fat. Set aside. In heavy skillet, cook the lamb fat over gentle heat (discard rendered-down pieces).
Toss meat in hot fat in the pan until slightly brown, then transfer to a Dutch oven. Quickly toss onions and carrots in the fat, and the pearl barley, if using, in layers in the pot, carefully seasoning each layer with freshly ground pepper and salt. Deglaze the skillet with 3 1/2 cups water, bring to a boil and pour into the pot. Lay the potatoes on top of the stew (they will steam while the stew cooks). Season potatoes, add the thyme and bring to a boil on the stovetop. Cover with a wax paper lid and pot lid. Transfer to oven or let simmer on the stovetop until the lamb is tender, about 1 1/2 hours, adding additional water if needed.
To make the roux: In saucepan, melt butter and cook all-purpose flour or cornstarch with rice flour in it for 2 minutes over low heat, stirring occasionally. Roux can be stored and used as required or can be prepared on the spot. It will keep at least 2 weeks in the refrigerator.
When the stew is cooked, pour off cooking liquid and reserve, degrease it and reheat in another saucepan. Thicken slightly by whisking in 1 tablespoon roux. Check seasoning, then add half the freshly chopped parsley and chives. Pour over meat and veggies. Bring stew back to a boil, then serve with remaining chopped herbs.
