In a small skillet, combine the garlic cloves and the oil. Over a low heat, caramelize the garlic until browned and soft, about 20 minutes.
Transfer garlic cloves to a blender or food processor. Add the vinegar and mustard. Blend until smooth. With the motor running, slowly pour in the reserved garlic oil. Season with salt and pepper, to taste.
Chop the lettuce into bite-sized pieces and put in a large salad bowl. Pour the dressing over the lettuce and toss to coat. Sprinkle some grated cheese on top and serve immediately.