Preheat oven to 375°. In a large ovenproof skillet over high heat, heat oil. Add corn; season with salt and pepper. Cook, tossing, until just cooked through, about 2 minutes. Transfer corn to a large bowl. Wipe out skillet (if using for nachos).
Add jalapeño and 1 tablespoon lime juice to corn and stir to combine. In a small bowl, stir sour cream, mayonnaise, and remaining 1 tablespoon lime juice; season with salt.
Layer chips and Monterey Jack in skillet or on a a large sheet pan. Bake until cheese is melty, about 5 minutes.
Top chips with corn mixture, mayonnaise mixture, Cotija, and cilantro.
