Heat olive oil in a large pot or Dutch oven over medium heat. Sauté the diced carrots and chopped onion until softened, about 5 minutes. Stir in minced garlic and cook for 1 minute until fragrant.

Pour in the chicken broth and bring the mixture to a boil. Stir in the orzo pasta, reduce heat to a simmer, and cook for 9 minutes, or until the pasta is tender.

Stir in the cooked shredded chicken and let it warm through for 2 minutes. Remove the pot from the heat completely.

In a medium mixing bowl, whisk the eggs vigorously until frothy. Gradually whisk in the fresh lemon juice.

Temper the egg mixture by slowly ladling 2 cups of the hot soup broth into the bowl while whisking continuously.

Pour the tempered egg-lemon mixture back into the soup pot, stirring constantly. Stir in the fresh dill, season with salt and pepper to taste, and serve immediately with crusty bread.