Melt butter in a Dutch oven over medium heat. Add onion and sugar; cover and cook 25 minutes or until golden brown, stirring frequently. Add mushrooms; cook 10 minutes or until browned, stirring frequently. Add barley; cook 2 minutes, stirring frequently. Remove from heat. Stir in soy sauce, salt, pepper, and thyme.
Preheat oven to 350°.
Bring broth to a boil in a medium saucepan. Pour broth over barley mixture; cover and bake at 350° for 1 hour or until barley is tender. Let stand 10 minutes. Garnish with thyme sprigs, if desired.