Melt the butter in a large pot over medium heat. Add the chopped onion and cook until translucent.
Add broccoli and chicken broth to the pot. Bring to a boil, then reduce heat and simmer until the broccoli is tender, about 10-15 minutes.
Puree the soup using a blender until smooth. Return to the pot.
Stir in the heavy cream and shredded cheddar cheese. Cook until the cheese is melted and the soup is heated through. Season with salt and pepper to taste.
Notes
This soup is best served warm and with crusty bread on the side.