Place rack in center position of oven. Preheat oven to 350°F.
Cut off any silk hanging out the ends. Trim any tips of leaves extending from sides. Do not peel.
Place ears of corn directly on oven rack. Cook for 30 minutes.
Remove corn from oven. Let cool for a few minutes before peeling back the husks. It’s hot so be careful!
Combine butter, zest from half the lime, and juice of whole lime. Stir in cilantro, salt, smoked paprika, and pepper. Transfer butter mixture to a serving bowl.