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1
Build a fire in your grill, leaving one side free of coals.
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2
When coals are covered with gray ash and the temperature is medium (you can hold your hand 5 inches above the coals for 5 to 7 seconds), you are ready to cook.
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3
(For a gas grill, turn all burners to high, lower cover and heat for 15 minutes, then turn burners to medium.)
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4
Meanwhile, make the dressing: Put the minced garlic into a bowl, and add the minced anchovies.
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5
Using a whisk, mix and mash these ingredients together until they form a paste.
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6
Add the mayonnaise and the mustard and whisk.
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7
Add the olive oil, whisking all the while, and then the vinegar.
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8
Season to taste with salt and pepper.
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9
Set aside.
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10
Make the salad: Drizzle the olive oil over the quartered heads of lettuce.
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11
Lightly grill these directly over the hot coals for 15 to 20 seconds on each side, until they are lightly golden, then remove to the cool side of the grill.
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12
Using a pastry brush or a small spoon, paint the dressing over the lettuce, making sure to get dressing between the leaves.
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13
Sprinkle the lettuce with Parmesan and cover the grill for 1 or 2 minutes to allow the cheese to melt and the lettuce to soften further.
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14
Remove lettuce to a platter and serve.
