Preheat grill to medium-high heat.
Brush corn with oil. Grill corn until charred in spots and tender, about 5 minutes on each side.
Remove from the grill and set aside to cool.
Place a saucepan with 5 cups of water and 1 tablespoon of salt onto a medium heat, bring the water to boil, and slowly stir in the polenta. Reduce the heat and continue to stir for about 5 minutes until thickened and creamy. Add the butter and blend into the mixture.
Stir in the cheese. Keep warm.
Cut the corn off of the cob and stir it into the cooked polenta. Season with salt and pepper, to taste, and serve warm.