Heat the oil in a large saucepan over medium heat. Add the leeks, carrots, and garlic, and sauté until the vegetables begin to soften, 5 to 7 minutes. Stir in the vegetable broth and orzo. Simmer until the orzo is almost al dente, 9 to 10 minutes. Remove from the heat.
Meanwhile whisk the egg yolks and lemon juice in a bowl until frothy.
When the orzo is almost done, take 1 cup of the hot broth and slowly pour it into the egg and lemon mixture, whisking constantly. Slowly whisk in 2 more cups of the broth. (It’s OK if some of the orzo gets whisked in too.)
Over medium-low heat, whisk the tempered egg and lemon mixture into remaining broth and orzo. ***Switch to a wooden spoon and, stirring continuously in a figure-eight motion, cook 1 or 2 minutes, just until the eggs slightly thicken the soup.
You want the soup to have a silky rich consistency. If the heat is too high you will get grainy pieces of egg suspended in a delicious vegetable broth. DO NOT BOIL.
Garnish with sprinkles of fresh parsley and lemon zest, if using.
Notes
Vegetable broth powder makes a quick, easy, and flavorful soup base.