Scrub the potatoes well and prick them in 5 to 6 places with a fork. Microwave on high until just cooked through, about 7 to 10 minutes. Set aside to cool, then peel and chop into bite-size pieces.
Meanwhile, heat the oil in the large saucepan over medium-high heat. Add the onion and sauté until it just begins to brown, about 2 to 4 minutes. Add the garlic and stir for 1 minute. Stir in the diced tomatoes, curry powder, and salt. Adjust the heat so it boils gently for about 10 minutes.
Add half of the sweet potatoes to the pot and stir. Puree the rest of the sweet potatoes with the broth and peanut butter until completely smooth. Add the puree to the pot and stir well to combine. Season with pepper and cook until hot. Serve with cilantro and chopped peanuts.