Heat olive oil in a large pot over medium heat.
Add diced 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 the mixture to a boil, then reduce heat and simmer for 15 minutes.
Use an immersion blender to puree the soup until smooth.
Return the soup to the pot and stir in heavy cream.
Gradually add shredded cheddar cheese, stirring until melted.
Season with salt and pepper to taste.
Serve hot, garnished with croutons if desired.