Heat olive oil in a large pot over medium heat. Add onion and cook until softened, about 5 minutes.

Add garlic and cook for 1 minute more.

Add broccoli florets and chicken broth. Bring to a boil, then reduce heat and simmer for 15-20 minutes, or until broccoli is tender.

Carefully transfer the soup to a blender (or use an immersion blender) and blend until smooth.

Return the soup to the pot and stir in heavy cream, cheddar cheese, and asiago cheese. Heat through, stirring until cheese is melted and smooth.

Season with salt and pepper to taste.