Preheat a gas or charcoal grill to medium-high (about 400–450°F). Clean the grates.
Pull back the husks of each ear without detaching them. Remove and discard all silk, then fold the husks back around the kernels to cover.
Place the corn on the grill, cover, and cook, turning every 5 minutes, until the husks are charred and the kernels are tender when pierced, 15–20 minutes.
Transfer to a platter. Carefully strip off the husks and any remaining silk, then brush the kernels all over with the melted unsalted butter.
Return the corn to the grill over direct heat and cook, turning occasionally, until lightly charred in spots, 2–4 minutes. Transfer to a platter and season with the kosher salt and black pepper.