Spread out sweet potato rounds in one thin layer using two rimmed baking sheets. Drizzle sweet potato rounds with olive oil and season with salt and pepper. Roast in the oven for 20 minutes, flip the rounds over, and return to the oven for another 15 minutes.
While the sweet potatoes are cooking, combine sour cream, cayenne pepper, and ground cumin in a small bowl. Set aside in the refrigerator until ready to serve.
Pile the cooked sweet potato rounds on one baking sheet. Top with a layer of black beans and cover evenly with cheese. Place the baking sheet in the oven and cook until the cheese in melted, approximately 3-5 minutes.
Remove from oven and cover with the diced green pepper, jalapeño, and chopped cilantro. Add the sour cream to the center of the nachos. Serve immediately.