Heat the oil in a large wide pot over medium heat. Add the cumin and onion and cook, stirring occasionally, until softened, about 3 minutes. Add the tomato paste, carrots and chipotles and cook, stirring, until the carrots brown, about 8 minutes.
Increase the heat to high and stir in the potatoes and squash, making sure they are well coated. Season generously with salt and pepper and continue to cook until the potatoes begin to soften, about 5 minutes more. Pour in the broth and bring to a boil.
Adjust the heat to maintain a simmer, cover and cook until the potato and squash are tender, about 15 minutes. Carefully puree the soup in batches in a blender until smooth or with an immersion blender in the pot. Rewarm over medium heat and adjust the seasoning with additional salt and pepper. Serve with a dusting of smoked paprika.
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