Use freshly shredded cheese: It melts more smoothly than pre-shredded cheddar.
Don't boil the cheese: High heat can cause the cheese and cream to separate.
Broccoli size: Chop the florets fairly small so they become tender quickly and are easy to eat.
For thicker soup: Simmer a few extra minutes before adding the cheese.
For a thinner soup: Add a little extra broth or milk.