Coat a nonstick medium pot with cooking spray (5 short sprays) and set over medium heat. Cook onions until they just begin to color, about 5 minutes. Add carrots, salt, pepper, paprika and mustard, stirring to mix. Cook until carrots begin to soften, about 2 minutes. Add potatoes and broth and half and half. Increase heat and bring to a boil, then reduce to simmer. Cook until potatoes are tender, about 20 minutes. Add cheese and stir to melt. Puree in a blender and return to heat to keep warm.
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