Dough:
Combine the flour and yeast in the work bowl of a stand mixer. Add the salt, water, 2 tablespoons of olive oil, and malted barley syrup. Start the mixer on low, using the hook attachment, and mix until the dough just comes together, approximately 1 1/2 minutes. Increase the mixer speed to medium and knead for 15 minutes.
Tear off a small piece of dough and flatten into a disk. Gently stretch the dough until thin. Hold it up to the light and look to see if the bakers windowpane, or a see-through, taut membrane has formed. The dough will be quite sticky, but manageable. Fold the dough onto itself and form it into a smooth ball. Oil the bowl of the stand mixer or other large canister with 2 teaspoons of olive oil. Put the dough in the bowl and roll it around to coat with the oil. Cover with a tea towel or plastic wrap and leave at room temperature to double in size, approximately 1 hour.
Split the dough into 3 equal parts using a knife or dough scraper. Flatten each piece into a disk on the countertop. Form each piece into a ball. Roll each ball on the counter until they tighten into rounds. Cover the balls with a tea towel and rest for 45 minutes.
To shape and cook the margherita pizza:
Heat a gas grill to high and make sure the grill grates are clean and free of debris.
Toss the tomato with 1 tablespoon of olive oil, the garlic, salt and red pepper flakes in a medium mixing bowl and set aside.
Lightly flour the countertop and flatten 1 of the dough balls. Use a rolling pin to roll the dough into a 16-inch round, rotating and stretching the dough as you go. Transfer the dough to a lightly floured pizza peel and stretch to re-shape if necessary.
Oil the grill grates and decrease the heat to medium. Brush the dough with 1 to 2 teaspoons of olive oil and flip onto 1 end of the hot grill, leaving room for the tomatoes on the grate . Put the prepared tomatoes on the grill, close the lid and cook until the bottom of the crust is golden brown and the tomatoes are softened, about 1 to 2 minutes. Brush the raw side of the dough with 1 to 2 teaspoons of olive oil, then immediately flip using the peel. Top with the grilled tomatoes, smashing and spreading the tomatoes to create a sauce . Sprinkle with the Parmesan, mozzarella and basil. Close the lid and cook until the bottom of crust is golden brown and the cheese has melted, another 1 to 2 minutes. Using the peel, remove the pizza to a cooling rack and let rest for 3 minutes before slicing.
To shape and cook the date and Prosciutto pizza:
Heat a gas grill to high and make sure the grill grates are clean and free of debris.
Layer 2 paper towels on a plate and lay the mozzarella slices in a single layer. Top with 2 more paper towels, a second plate, and a 2 pound weight. Set aside at room temperature for 20 minutes.
Meanwhile, lightly flour the countertop and flatten 1 of the dough balls. Use a rolling pin to roll the dough into a 16-inch round, rotating and stretching the dough as you go. Transfer the dough to a lightly floured pizza peel and stretch to re-shape if necessary.
Oil the grill grates and decrease the heat to medium. Brush the dough with 1 to 2 teaspoons of olive oil and flip onto the hot grill. Close the lid and cook until the bottom of crust is golden brown, for 1 to 2 minutes. Brush the raw side of the dough with 1 to 2 teaspoons of olive oil, then immediately flip using the peel, brush with remaining 1 to 2 teaspoons of olive oil, and top with the Parmesan , prepared mozzarella, prosciutto, dates and thyme . Close the lid and cook until the bottom of crust is golden brown and the cheese has melted, about 1 to 2 minutes. Using the peel, remove the pizza to a cooling rack and rest for 3 minutes before slicing.
To shape and cook cracker pizza:
Lightly flour the countertop and flatten 1 of the dough balls. Use a rolling pin to roll the dough into an 11 by 17-inch rectangle to fit a standard, stainless steel cooling rack. Lay the dough sheet onto the rack and gently stretch around the edges, pinching to hold in place. Brush the dough with 1 to 2 teaspoons of olive oil. Season with salt and pepper, to taste. Attach the Vise-Grips to 1 end of the cooling rack to use as a handle. Turn a gas burner on high. Hold the rack about 2 inches above the flame, and move back and forth constantly until the bottom is golden brown, about 3 to 4 minutes. Carefully turn the dough over, brush with 1 to 2 teaspoons olive oil and season with additional salt and pepper, if desired. Cook, as before, until golden brown, an additional 2 to 3 minutes.
