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Preheat the oven to 475°F with a rack in the center.
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Transfer the prepared Flaky Puff Crust Pizza dough to an ungreased 13" x 18" Crispiest Crust Pizza Pan (see "tips," below for alternative pan instructions), and stretch and push the dough toward the edges. Cover and let the dough rest for 15 minutes.
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Gently push and stretch the dough as necessary so that it touches all edges and corners of the pan; it should reach about halfway up the side walls. Re-cover the dough and let it rest for 15 to 30 more minutes, until the dough is visibly puffy around the edges. Meanwhile, prepare the toppings in the next step.
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To prepare the toppings: Wash and dry the tomatoes. Slice the tomatoes so you have twelve 1/8"-thick slices.
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In a medium bowl, toss the tomatoes and salt. Transfer the tomatoes to a colander, place the colander over the bowl, and let stand at room temperature for 15 minutes, stirring gently and occasionally to help the tomatoes release their juice. Pat the tomatoes dry to remove excess moisture. Reserve the drained tomato liquid.
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To top and bake the pizza: Sprinkle the Parmesan over the dough, then evenly distribute the grated mozzarella, cubed mozzarella, and bacon on top. Place the 12 tomato slices on top of the cheese and bacon, arranging in a 3 x 4 pattern; the goal is to have one tomato slice on each piece of pizza.
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Bake for 15 to 17 minutes, until the cheese is melted and browned in spots; any exposed dough should be golden brown. (Want to avoid large bubbles? Check on the pizza about halfway through baking and pop any especially big bubbles with the tip of a sharp knife, then continue baking.) While the pizza bakes, prepare the garlic-basil oil.
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To make the garlic-basil oil: In a small bowl, combine all of the ingredients. Set aside until the pizza is done baking.
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To make the mayonnaise drizzle: In a separate small bowl, mix together the mayonnaise, lemon juice, and 1 teaspoon of the reserved tomato liquid. Add additional reserved tomato liquid, 1/2 teaspoon at a time, until you reach a drizzleable consistency. Stir in the black pepper and set aside until the pizza is done baking.
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Remove the pizza from the oven and use a spatula to unstick any cheese around the edges of the pan. Transfer it to a wire rack (a Giant Spatula is a helpful tool here) and let the pizza cool slightly, 3 to 5 minutes, before slicing.
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To finish the pizza: In a large bowl, toss the lettuce with 3 to 5 teaspoons of the garlic-basil oil, to taste. (Reserve excess for another use.) Evenly distribute the lettuce over the top of the sliced pizza and finish with the mayonnaise drizzle.
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Storage information: BLT Pizza that has been topped with lettuce and mayonnaise is best enjoyed the day it’s made. Save any untopped pizza, refrigerated, in an airtight container for several days. To reheat the leftover pizza, wrap a single layer of slices in an aluminum foil packet. Heat in a 350°F oven until warmed through, about 10 minutes, then top with lettuce and finish with the mayonnaise drizzle.