In a large pot, heat olive oil. Sautee onion and carrot on medium low heat for about 10 minutes
Pour in the chicken broth and roughly chopped chicken breast. Bring it to boil and add in orzo. Simmer until the chicken and orzo are tender, for about 20 minutes.
Mix milk and flour in a bowl until smooth and pour it into the pot. Stir occasionally until the soup boils and thickens.
Bring it to the lowest heat and let it simmer for about 10 minutes. Meanwhile season it with salt and pepper.
Finally toss in parsley and spinach. Pour lemon juice and stir.