Roughly chop the onion, celery, garlic and wash the parsley. In a deep saucepan, add the water along with the stock cube, onion, celery, garlic, and parsley. Set over medium heat and bring to a boil.
Carefully add the chicken to the broth. Keep on a steady simmer for 30 minutes until the chicken is poached and fully cooked through. Remove from the heat and take out the chicken and shred it. Set it aside, cover, and keep warm.
Discard the onion, celery, garlic, and parsley and strain the broth through a sieve. Return the broth to the saucepan. Juice the lemons. Thoroughly whisk the lemon juice and eggs together in a medium bow or jug. While whisking, pour 2 ladlefuls of hot broth into the lemon egg mixture, one at a time to acclimatize the egg and prevent it from splitting/ curdling.
Slowly pour the lemon egg mixture back into the main pot of broth and whisk together quickly. Add the arrowroot powder into a small bowl with 2 tablespoons of water or broth and stir to combine. Pour into the broth and set again over medium heat.
Keep whisking until the sauce thickens, about 10-15 minutes. Add in the cauliflower rice and shredded chicken and stir through. Taste for salt. Ladle into bowls and serve with a drizzle of good quality extra virgin olive oil and a grind of black pepper.