Remove the dry outer leaves of the corn cobs. Peel back the additional layers, keeping them attached. Remove the silk from the cobs.
In a small mixing bowl, stir together the butter, basil, and honey until well combined.
Slather a scant amount of butter on the cobs until covered. Rewrap the husks to cover the cob, twisting the top to make sure it stays closed.
Grill the corn over medium heat until lightly charred on all sides and the corn is tender, about 5 to 10 minutes. Remove from the heat and set aside until cool enough to touch. Remove the husks and serve alongside the remaining honey basil butter.