Heat oven to 450 degrees Fahrenheit. In a bowl, toss the sweet potato with 2 teaspoons of oil to coat thoroughly, lay out flat on a baking sheet, and bake for 20 minutes until pieces are tender but not browned. Reduce oven to 350 degrees.
Bring water to a boil for the pasta. Cook according to package directions, and simply add the broccoli 30 seconds (if chopped small) to 1 minute (if slightly bigger pieces) before the pasta is done to quickly cook it. It will turn bright green. Drain. (Conversely, you could steam it separately, for 5-7 minutes, or until tender and bright green.)
Meanwhile, while waiting for water to boil, combine one heaping cup of roasted sweet potato with 2 cups of almond milk in a blender. Process until smooth. Reserve any remaining sweet potato to use as topping for pasta. Set aside the sweet potato milk.
Next, heat a skillet over medium heat, add the 3 tablespoons of oil and slowly add the flour, whisking constantly until thoroughly combined. Continue whisking about 3-5 minutes, taking care not to burn the flour. A nutty aroma will develop, which is when you can stir in the remaining ingredients: the sweet potato milk mixture, salt, garlic, hot sauce, mustard, soy sauce, and lime juice. Whisk often, bring to a boil, and then down to a simmer for about 10 minutes, or until pasta is done. The sauce will cook down and get thick.
After the pasta and broccoli have been drained, pour into the skillet with sweet potato sauce, and if you have additional sweet potato cubes, add them as well. Stir well to coat.
Transfer everything to a casserole dish and bake in the oven at 350 degrees for 20 minutes. To serve, top it with additional green chiles, chickpea crumbs, and a tiny bit of hot sauce for color.
If you want to speed this recipe up, you can omit the last step of baking the cooked pasta. It's still delicious without baking.