Barley lends a nice body to the chicken stock. Giving half the soup a quick puree makes it extra creamy.
In a medium saucepan, bring stock, 3 cups water, barley, ramp whites, and celery to a boil. Reduce heat and simmer until barley is tender, about 45 minutes.
Stir in ramp greens. Transfer half of soup to a blender and puree until smooth. Return to pot, stir to combine, and season with salt and pepper.