Have you ever grilled lettuce? If not, get ready for a delicious surprise!
With a silicone basting brush, lightly brush the cut sides of the lemons with olive oil and place cut side down on the grill. Cook until the lemons are slightly charred, about 3-4 minutes. Remove and let cool. Slice the head of lettuce in half lengthwise and very lightly brush with olive oil on both sides. Place cut-side down on the grill and cook until blackened and wilting in spots, about 3-5 minutes. Flip and repeat on the other side. Remove and let cool. Place the baguette slices on the grill and lightly toast on both sides, about 2 minutes per side. Juice the grilled lemons into a medium bowl; you'll get about 1/4 cup juice. Whisk the lemon juice together with the garlic, mustard, Parmesan, salt, pepper and remaining 1/2 cup olive oil. Roughly chop the lettuce and place in a serving bowl. Tear the toasted baguette slices into bite-size chunks and add to the bowl. Serve with the dressing and additional grated cheese for guests to assemble to their tastes.