½ cup all-purpose flour
Kosher salt
Freshly ground pepper
2 pounds skinless, boneless chicken breasts (cut into 1 1/-inch pieces)
¼ cup plus 1 tablespoon vegetable oil
2 carrots (sliced 1/4 inch thick)
2 celery ribs (sliced 1/4 inch thick)
1 large leek, white and pale green parts only (thinly sliced)
1 garlic clove (minced)
1 ¾ cups pearled barley
6 cups chicken stock
1 cup water
¼ cup chopped dill
2 tablespoons fresh lemon juice
¼ cup chopped tarragon
½ cup freshly grated Parmigiano-Reggiano cheese (1 1/2 ounces)