Preheat the oven to 400°F. Slice the tops off the garlic heads to expose the cloves. Place the garlic heads and cauliflower florets on a baking sheet. Drizzle with 1 tablespoon olive oil and sprinkle with half the salt and pepper. Roast for 25 minutes until the cauliflower is tender and the garlic is soft and golden.

While the vegetables roast, heat the remaining tablespoon of olive oil in a large pot over medium heat. Add the diced onion and cook for 5 minutes until softened.

Squeeze the roasted garlic cloves into the pot. Add the roasted cauliflower, vegetable broth, thyme, and remaining salt and pepper. Bring to a simmer.

Use an immersion blender to puree the soup until smooth. Add 3 cups of the broccoli florets and simmer for 8 minutes until the broccoli is tender but still bright.

Stir in the remaining 1 cup of broccoli florets and cook for 2 more minutes. Ladle into bowls and top with chopped parsley.