- In a large pot over medium heat, saute garlic for one minute, until fragrant.
- Add the chicken broth, heavy cream, and chopped broccoli. Increase heat to bring to a boil, then reduce heat and simmer for 10-20 minutes, until broccoli is tender.
- Add the shredded cheddar cheese gradually, stirring constantly, and continue to stir until melted. (Add 1/2 cup, simmer and stir until it melts fully, then repeat 1/2 cup at a time until all the cheese is used up.) Make sure to keep it at a very low simmer and avoid high heat, to prevent seizing.
- Remove from heat immediately once all the cheese melts.