In a large pot, heat the olive oil over medium heat. Add the diced onion and sauté until translucent, about 5 minutes. Stir in the minced garlic and cook for an additional minute until fragrant.
Add the cubed chicken to the pot and cook until browned on all sides, about 5-7 minutes.
Pour in the chicken broth and bring to a boil. Add the broccoli and cauliflower florets, dried thyme, salt, and black pepper. Reduce the heat to a simmer and cook for 15-20 minutes, or until the vegetables are tender.
Stir in the heavy cream and Parmesan cheese, mixing well until the cheese is melted and the soup is creamy.
Taste and adjust seasoning if necessary. Serve hot, garnished with fresh parsley.