Gather all ingredients.
In a large pot over medium heat, melt the butter. Add the chopped onion and cook, stirring occasionally, until softened.
Stir in the broccoli, then add the chicken broth. Bring to a simmer and cook until the broccoli is tender (10-15 minutes).
Reduce heat, add cheese cubes and stir until melted. Stir in milk and garlic powder.
In a small bowl, mix 2 tbsp of cornstarch with 1 cup of water until smooth. Stir into the soup, cook while stirring frequently, until it thickens.
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