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In a large saucepan, melt butter over medium heat.
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Add onion and cook until golden, about 10 minutes, stirring occasionally.
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Whisk in flour and salt.
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Gradually stir in milk, chicken broth, and water.
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Add cauliflower and heat to boiling over high heat.
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Reduce heat to low; cover and simmer until cauliflower is tender, about 15 minutes. (Be careful how high you have the heat here as it tends to boil over easily with the milk.)
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In blender (with center part of blender cover removed to allow steam to escape),or with an immersion blender, blend cauliflower mixture at low speed in small batches until very smooth.
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Return cauliflower mixture to saucepan; heat over medium heat until hot, stirring occasionally.
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Remove saucepan from heat; stir in mustard and 1 1/2 cups cheese until melted and smooth.
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Serve soup with remaining cheese as a garnish.