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Bring a large pot of salted water to a boil over high. Add chopped yam and brown sugar; cook, stirring occasionally, until tender, 20 to 25 minutes, being careful not to overcook. Drain and return yam to pot. Using a potato masher, mash yam while still steaming. Add red palm oil, canola oil, thyme, garlic, corn flour, and salt. Mash until mixture is fully combined, smooth, and evenly colored, about 5 minutes. Let mixture stand at room temperature until cool enough to handle, about 10 minutes.
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Divide yam mixture evenly into 10 pieces (about 3 1/2 ounces each). Shape each piece into a 3/4-inch-thick, 3-inch-wide patty.
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Heat a large pan over medium, and add canola oil to a depth of 1/8 to 1/4 inch. Add 5 patties to hot oil; fry until golden and crisp, about 5 minutes per side. Transfer cooked patties to a rimmed baking sheet or a platter, and cover loosely with aluminum foil to keep warm while cooking remaining patties. Repeat process with additional oil and remaining patties. Top patties with soft-cooked eggs; sprinkle with chiles, cilantro, and onion.
Photo by Victor Protasio / Food Styling by Torie Cox / Prop Styling by Claire Spollen
Notes
Find puna yams and red palm oil at specialty food markets, or order from olasfoodsmarket.com.