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Bring a small pot of water to a boil. Add sweet potato and cook, covered, until fork-tender, about 5 minutes. Drain and mash with a pestle or potato masher until completely smooth.
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Meanwhile, heat oil in a large nonstick pan over medium heat. Add onion, serrano, cumin, oregano and salt; cook, stirring frequently, until the spices are fragrant and the onion is tender, 3 to 4 minutes. Transfer to a bowl. Wipe out the pan.
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To assemble quesadillas, spread about 1/4 cup mashed sweet potato in a thin layer on one half of each tortilla. Top with about 1 tablespoon onion mixture and 1/4 cup cheese. Fold the bare half of the tortilla over the filling.
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Heat the pan over medium-low heat. Cook 2 quesadillas, flipping once, until crispy and golden and the cheese has melted, 5 to 6 minutes. Repeat with the remaining quesadillas. Top with cilantro.