Place corn, still in their husks, directly on the middle oven rack. Cook until corn is tender and heated through, about 40-45 minutes. (Note: If you'd rather not put the corn directly on the rack, you can also cook it on a baking sheet for the same amount of time).
While corn cooks, combine mayonnaise, sour cream, cilantro, garlic, and cotija cheese in a small bowl and mix until combined and mostly smooth.
When corn has cooked, peel down and discard husks. Using a spatula, spread a generous helping of the sour cream mixture over all sides of the corn. Place corn on a serving plate and drizzle with lime juice. Finish by sprinkling smoked paprika and more fresh cilantro on top.
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