In a large pot, heat the olive oil over medium heat.

Sauté the diced onion until it becomes translucent, about 3-5 minutes.

Stir in the minced garlic and cook for another minute.

Add the chopped broccoli to the pot and stir well.

Pour the vegetable broth into the pot and bring to a boil.

Cook the broccoli until tender, typically around 10 minutes.

Use an immersion blender to puree the soup until smooth.

Return the smooth soup to the pot and stir in the heavy cream and shredded cheddar cheese.

Add salt, pepper, and dried thyme if using.

Serve the soup hot, garnished with additional cheddar cheese if desired.