Place chicken broth in a large saucepan, add a handful of quick-cooking barley, and cook until barley is tender, about 12-15 minutes. Set aside to cool.
In a mixing bowl, add the plain yogurt, and whisk in one beaten egg until well combined. Set aside.
Meantime, in a skillet, melt 2 Tbsp butter, and saute the minced onion, over a low heat until onions begin to caramelize, about 5-7 minutes; stir in 1 Tbsp. dried, crushed mint. As soon as the onion and butter turn a light brown, remove skillet from heat.
Once the chicken broth and barley have cooled, vigorously whisk the yogurt-egg mixture into the saucepan, then stir in the onion-mint mixture. Season with salt according to your taste. Heat ever-so gently, stirring constantly, until a slight simmer has been reached, about 5 minutes.
Serve immediately.