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Bring a large pot of water to a boil with a splash of olive oil and pinch of salt. Cook the pasta according to the instructions on the package until al dente, and drain thoroughly. Transfer the pasta back to the pot, and stir through the tablespoon of olive oil. Set aside.
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To make the sauce, heat 1 tablespoon olive oil in a small skillet over medium heat and sauté the onions and garlic for about 5 minutes, until soft and translucent. Allow to cool slightly.
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Throw the broth, onion mixture, lemon juice, cashews, carrots, nutritional yeast, salt, mustard, pepper, and smoked paprika into your KitchenAid® Pro Line® Series blender and blast on high for 40 to 60 seconds, until smooth and creamy. Tweak salt, pepper, and paprika to taste.
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Pour the sauce onto the pasta, add the steamed broccoli, and gently stir to combine. On low heat, warm gently. Transfer to a shallow baking dish and serve family style, or portion out into bowls. Season to taste.