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Melt butter over medium heat in large saucepan
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Add onion and garlic and cook for 5 minutes - don't let the garlic brown.
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Stir in broccoli and chicken broth.
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If you desire less chunks, remove 1/2 of the soup to a blender and process for 10-15 seconds. If you want a chunkless soup, process all of the soup.
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Return soup to the saucepan and bring to a boil and simmer until broccoli is tender, 10 to 15 minutes.
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Meanwhile whisk flour into milk until dissolved.
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Stir into soup stirring frequently until thickened.
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Reduce heat, and stir in cheese until melted and heated through.
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Season with salt and white pepper to taste.