Warm a large soup pot over medium heat and pour in the olive oil.
Add diced carrots, onion, and minced garlic to the pot and cook until they soften and release their aroma, about 10 minutes, taking care not to let the garlic brown.
Pour in the chicken broth and bring everything to a gentle simmer.
Stir in the whole wheat orzo and let it cook for several minutes until it becomes tender.
Mix in the shredded cooked chicken and then remove the pot from heat.
In a small bowl, beat together the eggs and freshly squeezed lemon juice.
Gradually ladle warm soup into the egg and lemon mixture to temper it, stirring gently.
Slowly pour the tempered egg mixture back into the soup pot, stirring continuously and steadily to create a smooth, creamy texture without curdling.
Finally, fold in fresh spinach, season with salt and plenty of black pepper, and add as much fresh dill as desired.
Taste and adjust seasoning before serving.