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1
Warm 2 tablespoons oil in a wide pan over medium heat. Add carrot, chayote, and onion with a pinch of salt and enough water to barely cover. Cook, stirring occasionally, until beginning to soften, about 5 minutes.
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2
Add green beans, zucchini, corn, serrano chiles, and remaining water. Continue cooking until all vegetables are tender but still holding their shape. Season with salt.
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3
Remove from heat. Cool slightly, then drain away any remaining liquid. Set filling aside.
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4
Divide masa into balls roughly 30–35 g each. Press each ball between sheets of plastic into a round approximately 9 cm (3.5 inches) across.
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5
Place a spoonful of filling on one half of each round, leaving a clear border. Fold the masa over to enclose the filling and press edges firmly to seal.
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6
Pour vegetable oil into a heavy skillet to a depth of about 1 cm. Heat to approximately 180°C (356°F). Fry quesadillas in batches, turning once, until golden and crisp on both sides, roughly 2–3 minutes per side.
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7
Drain briefly. Arrange on romaine leaves, spoon salsa verde over the top, and scatter crumbled queso fresco across each portion. Serve at once.