Saute onion and garlic in butter until onion is soft.
Add chicken broth, salt, pepper, and broccoli. Bring to a boil, cover and simmer 45 mins or until broccoli is soft.
Next, add heavy cream... then add the shredded cheddar. Mix well, if you would like to thicken it up turn up the heat and add a tablespoon of cornstarch. Stir constantly for a few minutes. Still not thick enough? Add another tablespoon or so to reach desired consistency.