Start off by heating some olive oil in a big Dutch oven or any large sturdy soup pot, over a medium-high flame. Toss in the carrots, celery, and onion for a quick sauté. Then, add the garlic and cook it just until it smells amazing but hasn't turned brown.
Pour in the chicken broth and crank up the heat to get it boiling. When it’s bubbling away, add the rice along with the salt and pepper. Lower the heat to a gentle simmer and let it cook for about 20 minutes, or until the rice is tender. Next, mix in the dill and the cooked chicken.
Now for the magic touch, the egg-lemon sauce. In a bowl, whisk the lemon juice and eggs together. To make sure the eggs don’t scramble, slowly drizzle in 2 ladles of the hot broth from your soup while whisking constantly. After it’s all smooth, pour this egg-lemon goodness into your soup, giving it a good stir, then take it off the heat right away.
Dish it up while it’s warm and serve it alongside your favorite bread to sop up all that deliciousness. Dig in and enjoy!