Cook the Chicken: Heat olive oil in a large pot over medium heat. Add the chicken pieces and cook for about 5-7 minutes, or until they are browned and cooked through. Remove the chicken from the pot and set aside.
Sauté Vegetables: In the same pot, add chopped onion and minced garlic. Cook for 3-4 minutes until the onion is translucent and the garlic is fragrant.
Add Vegetables: Stir in the cauliflower, broccoli, carrots, and peas. Cook for another 5 minutes, allowing the vegetables to start softening.
Simmer Soup: Return the chicken to the pot and pour in the chicken broth. Bring to a boil, then reduce the heat and let it simmer for about 15 minutes, or until the vegetables are tender.
Finish the Soup: Stir in the heavy cream, dried thyme, salt, and pepper. Simmer for an additional 5 minutes to heat through and let the flavors meld together.
Serve: Ladle the soup into bowls and enjoy hot.