Bring a large pot of lightly salted water to a boil. Cook macaroni in the boiling water, stirring occasionally, until tender yet firm to the bite, about 8 minutes. Drain.
Place potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer until tender, about 20 minutes. Drain. Peel and finely chop potatoes when cool enough to handle.
Combine potatoes, onion, carrot, and garlic in a small pot over medium heat. Add 2 tablespoons water and cook until soft enough to blend and water is mostly evaporated, about 3 minutes. Remove from heat. Transfer sauce to a blender. Add 3/4 cup water, cashews, soy milk, nutritional yeast, lemon juice, salt, paprika, and cayenne. Cover the blender and hold lid down with a potholder; pulse a few times before leaving on to blend until smooth.
Heat 2 tablespoons water in a nonstick pan over medium heat. Add broccoli and cook until soft but still a little crunchy, about 5 minutes. Transfer to a large serving bowl. Pour sauce in and mix until thoroughly coated.