In a large pot, heat 2 tablespoons of olive oil over medium heat. Once shimmering, add the diced boneless skinless chicken thighs. Brown them for about 5 minutes, stirring occasionally until the chicken is golden on all sides.

Next, stir in the chopped onion and minced garlic into the pot. Sauté for 2-3 minutes until the onion becomes translucent and fragrant, stirring frequently to avoid burning.

Now, incorporate the cauliflower florets and chopped celery into the mix. Cook these for 3-4 minutes, stirring until they start to soften.

Add 4 cups of low-sodium chicken broth and sprinkle in the dried thyme. Increase the heat to bring the mixture to a rolling boil, then reduce to a gentle simmer. Allow it to simmer uncovered for about 15-20 minutes, or until the vegetables are tender.

Once the vegetables are tender, gently stir in 1 cup of heavy cream. Season the soup with salt and pepper to your liking, and let it simmer again for an additional 5 minutes.

Ladle the warm soup into bowls and garnish each serving with fresh parsley.