In a large pot, heat 2 tablespoons of olive oil over medium heat. Add 1 pound of diced boneless, skinless chicken thighs. Cook for about 5 minutes, stirring occasionally, until the chicken is nicely browned and cooked through.

Stir in one chopped onion and 3 minced garlic cloves, sautéing for 2-3 minutes until the onion becomes translucent.

Add 4 cups of cauliflower florets and 1 cup of chopped celery to the pot. Cook for 3-4 minutes until the vegetables are slightly tender.

Pour in 4 cups of low-sodium chicken broth and sprinkle 1 teaspoon of dried thyme. Bring to a boil, then reduce to a simmer. Cook for 15-20 minutes until the vegetables soften.

Mix in 1 cup of heavy cream, stirring to combine. Season with salt and pepper to taste, and let it simmer gently for an additional 5 minutes.

Ladle the soup into bowls and garnish with chopped fresh parsley. Serve hot.