Heat grill or broiler (medium heat). Trim fat and gristle from steak. Grill or broil steak 12 to 14 minutes, turning once. Don't overcook. Remove from heat and let rest while preparing vegetables.
In a large stock pot, saute vegetables in oil over medium-high heat until lightly brown, about 10 minutes. Add barley and cook an additional 5 minutes.
Pat steak dry with paper towels. Cut into half-inch pieces and add to pot. Then add vinegars, stock, herbs and spices.
Bring to a boil and simmer 1 hour, until barley is cooked and stew has thickened considerably.