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Put the oil in a large pot over medium heat.
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Once warm, add the onion, carrot, celery and some salt and pepper and cook, stirring occasionally, until the vegetables begin to soften, about 5 minutes.
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Add the garlic in after 3 minutes of cooking the mirepoix.
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Add the cauliflower, beer, stock, bay leaf and cayenne.
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Bring to a boil, then adjust the heat so the mixture bubbles only slightly.
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Cover and cook until the cauliflower is good and tender - about 10 to 15 minutes.
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Remove and discard the bay leaf.
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Purée the soup in batches in a blender until smooth.
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Return to the pot.
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Stir in the mustard and remaining salt and pepper.
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In a bowl, toss together the cheddar cheese and cornstarch together and mix well.
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Add the cheese mixture to the soup a handful at a time, stirring all the while, until it’s well incorporated and the soup is smooth.
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Serve hot, garnished with the parsley.