In a medium skillet over medium-high heat, combine the water, potato, carrots, garlic, onion, chile (if using), tomato, and cashews. Cover the skillet and cook 18 to 20 minutes, or until the potato is very tender. Let the mixture cool slightly.
Meanwhile, bring a medium saucepan of water to a boil over high heat. Add the broccoli and cook for 2 minutes. Drain the broccoli and set aside. Alternatively, you can add the broccoli to the cooking pasta pot in the last two minutes.
Combine the potato mixture (along with its liquid), mustard, soy sauce, nutritional yeast, lemon juice, oil, paprika, and sriracha (if using) in a blender. Blend for 1 minute, let the mixture rest for 1 minute, and blend again until smooth.
Transfer the mixture to the saucepan over medium heat. Add the salt, white pepper, and 1/2 teaspoon of the black pepper, stirring to combine. Add some additional water to adjust the consistency if the sauce is too thick.
Bring the sauce almost to a boil. Taste and adjust the seasonings. Add the elbow pasta and broccoli. Stir to combine, cover the saucepan, and cook for 3 minutes. Let the mixture sit for 2 minutes. Add the remaining 1 teaspoon black pepper. Sprinkle some more pepper on each serving, if desired.