Heat oven to 450 degrees. In a bowl, toss the sweet potato with 1 tablespoon of oil to coat thoroughly, lay out flat on a baking sheet, and bake for 20 minutes until pieces are tender but not browned.
Bring water to a boil for the pasta. Cook according to package directions, and simply add the broccoli 30 seconds (if chopped very finely) to 1 minute (if slightly bigger pieces) before the pasta is done to quickly cook it. It will turn bright green. Drain.
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 coconut oil and slowly add 1/3 cup tapioca 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, 2 tsp salt, 1 chopped garlic clove, and 1 teaspoon each of 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 add additional sweet potato cubes, add them as well. Stir well to coat. Serve.
After coating the pasta and veggies in sweet potato sauce, you can transfer to a casserole dish and bake in the oven at 350 for an additional 20 minutes if you desire.