Heat your grill to a medium-high setting.
In a bowl, blend the softened butter with smoked paprika, chopped garlic, sea salt, and black pepper until smooth.
Generously coat each ear of corn with the smoky garlic butter.
Wrap each ear of corn snugly in aluminum foil, sealing the edges tightly.
Place the foil-wrapped corn directly onto the grill grates and cook for about 15 to 20 minutes, turning occasionally.
Once the corn is tender, carefully take it off the grill and unwrap the foil.
Serve immediately, garnished with fresh parsley and accompanied by lime wedges.