Melt the butter in a dutch oven or stock pot over medium heat. Sauté the onion and garlic for about 2 minutes until the onions are translucent.
Add the finely chopped broccoli (remember, no big pieces!) and pour in the chicken broth. Stir and cover, reduce the heat to medium low and allow the broccoli to simmer about 15 minutes or until tender.
Stir in the cubbed cream cheese, shredded cheddar cheese and heavy cream. Continue stirring until the mixture is smooth and the cheese has melted.
Fold in the shredded chicken and add salt and pepper to taste.