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Trim the ends of each ear of corn while leaving the husks intact. Place the corn in a large bowl or container of water and keep it fully submerged for at least 30 minutes. This helps prevent the husks from burning too quickly on the grill.
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While the corn is soaking, mix the softened butter with the chopped chile, chile-lime seasoning, lime zest, and kosher salt in a small bowl. Stir until everything is evenly combined, then leave the butter at room temperature.
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Preheat your grill to medium heat, around 350°F to 400°F.
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Place the soaked corn directly onto the grill grates with the husks still on. Grill for about 20 minutes, turning every 10 minutes until the husks become lightly charred and the corn is tender inside.
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Allow the corn to cool for about 2 minutes before handling. Carefully peel back the husks, remove the silky strands, and leave the husks attached to use as a natural handle if desired. Generously spread the warm corn with the prepared chile-lime butter.
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Sprinkle each ear with crumbled Cotija cheese and freshly chopped cilantro. Serve immediately while warm.