Drain tofu and place in a dish towel and a heavy skillet or book on it to drain water for about 45 minutes. Then, cut into 1 inch cubes and pour marinade over it and let stand for 25 minutes.
Prepare marinade for tofu with brown sugar, 2 tablespoons of soy sauce, 1 teaspoon of fresh minced ginger, 1 teaspoon dark sesame oil and garlic clove minced.
Preheat oven to 375˚. Once tofu has marinated, bake for about 30 minutes, turning after 15 minutes. Cool and set aside.
To prepare barley: heat one teaspoon of sesame oil in a heavy saucepan over medium-high heat. Add barley and toast for about 3 minutes stirring frequently. Add 5 cups of water and ½ teaspoon of salt; bring to a boil. Reduce heat and simmer for about 45 minutes or until barley is tender. Drain, cool and set in a large bowl.
Cook green beans for about 3 minutes or until crisp-tender, drain and run under cold water. Add to bowl with barley.
Slice mushrooms thinly and cook on a pan with sesame oil. Add to bowl with barley. Slice scallions thinly. Add to barley and green beans.
Combine 1 tablespoon of sesame oil, rice wine vinegar, honey, 2 teaspoons of minced ginger, 1 minced garlic in a small bowl stirring with a whisk. Drizzle mixture over barley and other ingredients. Serve warm or chilled.