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Add butter to a large Dutch oven or stock pot. Heat over a medium/low flame until melted. Add the flour and whisk to combine.
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Add garlic and whisk to combine. Reduce heat to low.
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Slowly stream in the heavy cream, beer, and stock while whisking. Gently increase the flame to medium. Bring to a simmer.
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Add in the broccoli and carrots. Stir to combine.
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Add the mustard, paprika, salt, and pepper. Stir to combine.
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Simmer for about 15 minutes over a medium/low flame, covered with a lid.
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Reduce heat to low and mix in almost all the cheese. Reserve some of the cheese for topping the soup when serving.