Heat a large soup pot over medium heat. Add olive oil, then sauté carrots, onion, and garlic until fragrant and tender, about 10 minutes.

Pour in chicken broth and bring to a simmer. Add the orzo and cook until just tender, about 4-5 minutes. Stir in shredded chicken and remove from heat.

In a small bowl, whisk eggs and lemon juice together. Gradually add a ladle of hot broth into the egg mixture while whisking constantly to temper the eggs. Slowly pour egg mixture back into the soup while stirring continuously until well incorporated and creamy.

Stir in spinach, salt, pepper, and dill. Adjust seasoning as needed. Serve hot.