In a pot over medium heat saute garlic for one minute or until fragrant.
Add the chicken broth, heavy cream, chopped broccoli and bring to a boil. Reduce heat and simmer until broccoli is tender, approximately 10-15 minutes.
Add the shredded cheddar gradually, stirring constantly, and continue to stir until melted. Simmer it low to prevent seizing. Remove from the heat and serve.