Heat the avocado oil in a 5-quart Dutch oven or heavy-bottomed stockpot over medium heat.
Add the chopped celery and onion. Sauté for 6 minutes, stirring frequently, until the onion is translucent and the celery has softened.
Stir in the minced garlic, dried thyme, and smoked paprika. Cook for 60 seconds until the aromatics release their essential oils and become fragrant.
Pour the chicken bone broth into the pot and increase the heat to medium-high to achieve a steady simmer.
Submerge the cubed chicken thighs and the riced cauliflower into the simmering liquid.
Reduce the heat to medium-low, cover the pot, and simmer for 12 to 15 minutes, or until the chicken reaches a minimum internal temperature of 165°F (74°C).
Remove the pot from the heat source and incorporate the salt and black pepper.
Garnish with fresh parsley and serve immediately.