For the llajua, combine tomato, locoto pepper, scallion, quirquiña (papalo) leaves, and 0.5 teaspoon of the salt in a mortar or blender; grind or pulse to a coarse, pourable sauce. If very thick, add 1–2 tablespoons cold water. Set aside.
Prep the components: scrub the potatoes and leave skins on; halve the corn on the cob; rinse the fava beans if needed; pat the fresh frying cheese dry and cut it into 4 even slices; measure the vegetable oil.
Place the cobs in a pot, cover with water by 1 inch, bring to a boil, then reduce to a lively simmer until the kernels are tender and juicy, 20–30 minutes. Keep warm in the hot water off heat.
In a second pot, cover the tubers with cold water and add the remaining 1.5 teaspoons. Bring to a boil, then simmer until a knife slides in easily, 20–25 minutes. Drain and keep warm.
Bring a small pot of water to a boil and add the legumes. Cook until bright green and just tender, 3–5 minutes. Drain; if the outer skins are tough, pinch and slip them off while warm.
Heat the measured oil in a large skillet over medium heat until shimmering. Add the sliced dairy and fry until golden on the first side, 2–3 minutes; flip and brown the second side, 1–2 minutes, until the center softens.
Divide the boiled tubers, cobs, and legumes among 4 plates. Top each with a fried slice.
Spoon some of the sauce over the plate or serve it alongside. Serve immediately while hot.