In a large stock pot, heat 2 tablespoons olive oil over medium heat. Sauté onions until soft and translucent, about 5 minutes. Add 1/4 cup dill, chicken broth, bay leaf and bring to a boil.

Add rice and reduce heat to medium low, and simmer about 10 minutes. Add carrots and asparagus and cook an additional 10-15 minutes, or until rice is cooked and vegetables are tender. Add chicken and continue to simmer on low while preparing egg and lemon juice mixture.

Meanwhile, in a separate bowl, combine egg, lemon juice and 2 tablespoons of water.

Slowly whisk about half a cup of the hot stock into the egg mixture, stirring constantly, to keep eggs from curdling.

Slowly whisk the egg/lemon broth back into the stock pot. Soup will thicken slightly. Turn off heat and remove bay leaf.

Add remaining fresh dill, and adjust seasoning with salt and pepper.