1. Divide dough into four equal parts and place each in a covered quart-sized deli container or a zipper-lock freezer bag. Allow to rest at room temperature for at least 2 hours before baking. Transfer tomatoes to a medium bowl and roughly crush by hand. Season to taste with salt and set aside. 

2. Adjust oven rack to 6 inches under broiler and place stone or steel on rack. Preheat oven to highest possible temperature (500 or 550°F) for at least 45 minutes. Alternatively, use a KettlePizza and Baking Steel grill insert. 

3. When ready to bake, turn one dough ball out onto a lightly floured surface. Gently press out dough into a rough 8-inch circle, leaving the outer 1 inch higher than the center. Gently stretch dough into a 10- to 12-inch circle, about 1/4 inch thick, by draping over knuckles and gently stretching. Transfer to floured wooden pizza peel. 

4. Preheat broiler to high. Spread a thin layer of crushed tomatoes over the pizza, leaving the 1-inch border around the edge. Spread 1/4 of mozzarella over pizza, followed by 1/4 of Parmesan, 1/4 of sliced soppressata, 1/4 of chilies, and 1/4 of basil leaves. Sprinkle lightly with salt and drizzle with 1 tablespoon olive oil. 

5. Transfer pizza to hot stone or steel and broil, rotating regularly for even cooking, until edges are puffed and lightly charred and bottom is crisp, 3 to 6 minutes total. Retrieve pizza with a metal peel and transfer to a cutting board. Allow to rest 1 minute. Meanwhile, switch oven back to 550°F to reheat stone or steel for remaining pizzas. 

6. Drizzle pizza with 1 tablespoon honey, slice, and serve. 

7. Repeat steps 3 through 6 for remaining pizzas.