Although quick and simple, these stuffed creminis leave a memorable impression.
Place mushrooms in a large bowl and toss with olive oil, salt, and pepper.
Light one chimney full of charcoal. When all charcoal is lit and covered with gray ash, pour out and spread the coals evenly over entire surface of coal grate. Set cooking grate in place, cover grill and allow to preheat for 5 minutes. Clean and oil the grilling grate. Place mushrooms on the grill, gill side up, and cook until mushroom caps brown and start to release their moisture, 3-4 minutes. Flip and continue to cook until mushrooms are slightly soft, about 3 minutes more. Remove mushrooms to a tray, gill side up, and let cool for 3-5 minutes.
Fill each mushroom with a spoonful of basil parmesan mayonnaise. Serve immediately.