Heat oil in a large casserole dish. Add shallots and cook for 5-6 mins until starting to soften and brown. Add leeks for 2 mins, then stir in swede, parsnips and carrots.
Pour in barley and wine, cook until wine has reduced by half. Add stock, bay, thyme, parsley and seasoning. Cover pan, bring to the boil, then simmer for 45 mins until barley and veg are tender. Stir occasionally to stop it catching.
Meanwhile, make the dumplings. Heat oven to 200C/180C fan/gas 6. Rub flour and butter together to form breadcrumbs. Add remaining ingredients and mix well. Sprinkle over 2 tbsp water, mix to form a soft dough. Divide into six and roll into balls. Dot on top of stew and transfer to oven. Cook, uncovered, for 20-25 mins until dumplings are golden.