How to Make It
Light a grill. Put the onions in a bowl and toss with 2 tablespoons of the olive oil. Season with salt and pepper. Set a perforated pan over the grill and add half of the onions. Cook over high heat, tossing with tongs, until lightly charred, about 3 minutes. Repeat with the remaining onions.
In a large, deep skillet, heat the remaining 1/4 cup plus 2 tablespoons of olive oil and add the garlic. Cook over moderately high heat until the garlic starts to brown, about 30 seconds. Add the mushrooms, celery, bay leaves and vinegar and stir well. Cover and simmer over low heat for 15 minutes, stirring a few times. Stir in the onions and transfer to a large bowl. Season with salt and pepper and let cool to room temperature. Discard the bay leaves, stir in the basil and serve.