Heat olive oil in a large pot over medium heat.
Add chopped onion and sauté until translucent, about 5 minutes.
Stir in minced garlic and cook for another minute.
Add broccoli florets and vegetable broth to the pot.
Bring to a boil, then reduce heat and simmer for 10-15 minutes until broccoli is tender.
Use an immersion blender to puree the soup until smooth.
Stir in the cream or coconut milk, mixing well.
Season with salt and pepper to taste.
Reheat the soup gently if needed.
Serve hot, garnished with grated cheese or fresh herbs.