In a large pot combine the potatoes, onions, garlic, chicken broth, water, salt, pepper, and thyme.
Bring to a boil then reduce heat to medium and cook for 15 minutes.
Stir in the broccoli and return to a boil.
In a small bowl whisk the flour and milk together until smooth. Stir into the soup along with the cream cheese. Mix well and cook for 3-4 minutes or until the soup has thickened.
Remove the soup from the heat and stir in the cayenne pepper and cheddar cheese. Mix until the cheese is melted.
Serve hot with additional cheese for topping.