Gently pull back the husks on each corn ear without detaching them, then remove all silk strands. Fold the husks back over the kernels to cover them. Place the corn in a large bowl or bucket and submerge completely in cold water. Let soak for 15 minutes to prevent husk burning and create internal steam during grilling. While soaking, gather your seasoning ingredients and set up your grilling station.

In a small bowl, combine the unsalted butter, olive oil, salt, black pepper, and smoked paprika. Mix while the butter is still slightly firm to create a thick paste that will stick to the corn. Preheat your grill to medium-high heat, approximately 400°F.

Remove the corn from the water and shake off excess liquid. Place the husk-wrapped ears directly on the preheated grill grates. Grill for 15 to 20 minutes, turning every 3 to 4 minutes to char the husks evenly on all sides. The husks will blacken in spots and you'll hear gentle steaming sounds—this is exactly what you want.

Using tongs, carefully remove the corn from the grill (husks will be very hot). Once cool enough to handle, peel away and discard all charred husks and any remaining silk. Reduce your grill heat to medium, around 350°F. Brush each naked ear generously with the seasoning paste, coating all sides thoroughly.

Return the seasoned corn to the grill. Cook for 10 to 15 minutes, turning every 2 to 3 minutes, until the kernels develop light char marks and caramelization. Transfer to a serving platter and brush with any remaining seasoning paste while still warm. Taste and adjust salt and pepper if needed. Serve immediately with lime wedges for squeezing over the corn.