Heat 1 1/2 teaspoons sesame oil in a large frying pan over medium-high heat.
Add red peppers and snow peas and stir-fry until tender crisp. The snow peas should hold a bright green colour. Remove vegetables onto a plate and reserve.
In the same pan add the remaining 1 1/2 teaspoons of sesame oil and stir fry the white portions of onions and garlic for 1 minute.
Stir in barley, 1/4 cup cilantro, 1 cup broth and bring to a boil.
Cook 3 minutes or until liquid is nearly absorbed, stirring constantly.
Add remaining broth, 1/2 cup at a time, stirring constantly until each portion is absorbed before adding the next. This step will take approximately 15 minutes and barley should be slightly al-dente. Use only 2 1/2 cups of broth unless more is needed to reach the al-dente consistency.
In a small bowl combine lime juice and next 6 ingredients (brown sugar through ginger); set aside.
If making ahead add chicken, peppers, snow peas, coconut milk and juice mixture to the barley. Stir mixture and cover.
At home reheat and bring to a boil. Reduce heat; simmer 5 minutes or until sauce thickens, stirring occasionally. Season with salt if needed. Stir in the remaining 1/4 cup cilantro and green onions. Sprinkle each serving with 1 tablespoon peanuts. If you have extra limes you can also use a wedge as a garnish.