In a slow cooker, place the chicken. Add the chicken broth, olive oil, oregano, and lemon zest. Cover and cook on HIGH for 3½ hours or LOW for 7 hours.

Add the cauliflower rice to the slow cooker. Cover and cook on HIGH for ½ hour or on LOW for 1 hour. Turn off the slow cooker.

In a small bowl, whisk the eggs, then slowly pour them into the slow cooker, stirring continually for about a minute, until the soup is slightly thickened and creamy.

Taste and season with sea salt and black pepper.

Divide the soup into 6 bowls and garnish with fresh parsley and lemon slices. Serve hot.