Preheat the broiler.
Place sweet potato noodles on a baking sheet. Drizzle with 2 tablespoons of olive oil and season with salt and pepper. Broil until slightly softened and brown in spots, about 5 minutes. Remove from oven.
In a small custard cup or bowl, mix together cumin, chili powder, and coriander.
Heat remaining 2 tablespoons of oil in a large skillet over medium heat. Add onion, bell pepper, and chile pepper. Cook, stirring occasionally, until softened, about 5 minutes.
Add corn, garlic, and cumin mixture to skillet. Continue cooking, stirring occasionally, until vegetables are tender, about 5 more minutes.
Add sweet potatoes, black beans, and water to skillet. Cook, gently tossing, until beans are warm and noodles are tender, about 2 minutes.
Remove from heat and serve with lime wedges.