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 and potatoes to the pot. Pour in chicken broth and bring to a boil.

Reduce heat and simmer for 15-20 minutes, or until potatoes and broccoli are 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, salt, and pepper.

Heat through, but do not boil. Serve immediately.