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1. Melt the butter in a large stockpot over medium heat.
2. Add the butter and onion and cook until the onion softens.
3. Add the broccoli and pour the chicken broth on top.
4. Simmer the mixture until the broccoli is fork tender, which takes about 12 to 15 minutes.
5. Lower the heat, add the cheese and stir until the cheese melts.
6. Add the garlic and milk and stir to combine.
7. Whisk together the cornstarch and water in a small bowl until dissolved.
8. Add the cornstarch mixture to the soup, stirring until thick.
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