Base: Heat large soup pot over medium heat. Add the olive oil. Add the carrots, onion, and garlic. Saute until fragrant and tender, about 10 minutes. (Be careful not to burn the garlic.)
Orzo: Add the broth and bring to a simmer. Add the orzo and cook for a few minutes until softened. Stir in the chicken and remove from heat.
Eggs: Whisk the eggs and lemon juice together in a small bowl. The idea here is to warm up the egg mixture slowly (without scrambling the eggs). Slowly add a scoop of the soup into the egg mixture. Then add your warmed egg mixture back to the soup pot – slowly, slowly, slowly, stirring constantly, until smooth and creamy.
Final touches: Finish by stirring in your spinach, salt, pepper, and dill and adjust seasonings to taste!