Preheat a grill to high.
Put the lettuce in a bowl. Pour the dressing over and toss well.
Divide the dough into 4 equal balls. On a floured board, stretch and roll the dough into thin discs with a rolling pin. The dough may also be stretched by hand, but rolling will give you a thinner crust.
Coat the rolled out dough with olive oil and place, oiled side down, on a very hot grill. This can be done indoors on a cast-iron stovetop grill pan that has been preheated over medium-medium high. When you start to see bubbles on the surface of the dough, turn it over. It should be slightly browned on the bottom. Brush each round with a generous tablespoon of the garlic paste and sprinkle with the thyme. Remove from the grill with tongs and top with the Caesar salad. Grate parmesan cheese on top, fold in half, and eat.
Preheat the oven to 375 degrees F.
Peel the outermost layers of skin off the heads of garlic. Cut off the top 1/3 of the heads to open the cloves. Save the small pieces of garlic for another use (see Chef's Note). Put the heads, cut sides up, in a small baking dish and pour the olive oil over them. Season with salt and pepper.
Cover tightly, place in the oven, and roast until about 3/4 cooked, about 45 minutes. Uncover and return to the oven until the cloves begin to pop out of their skins and brown, about 15 minutes. Let cool.
When cool enough to handle easily, squeeze the roasted garlic into a small bowl. Press against the skins very well to get out all the sweet roasted garlic you can. Add the oil from the baking dish and mix well until a paste forms. Store, tightly covered, in the refrigerator, for up to 1 week.
It is hard to have too much roasted garlic around. You can roast the little bits from the tips of the garlic heads. Put them in a separate small baking container, such as an individual custard cup. Season with salt and pepper, douse with olive oil, cover, and place in the oven to bake along with the whole garlic heads. Depending on their size, they will be soft and browned in about 1/2 the time needed for the whole heads. The little pieces make a good "cook's snack" while preparing dinner, or can be squeezed into tomato sauce or onto pasta.