Remove dough from refrigerator and allow to rest in proofing containers, covered, at room temperature for 1 to 2 hours before baking. Dough temperature should reach 60°F (15.5°C) before stretching and baking; exact timing will depend upon ambient temperature.

Meanwhile, in a small bowl, combine 4 teaspoons parsley, biber salçasi, tomato paste, garlic, allspice, paprika, cumin, 1 teaspoon salt, and ¼ teaspoon pepper. Stir with spatula until smooth paste forms. Add lamb and knead gently with hands until thoroughly combined. Cover and refrigerate until needed; mixture can be refrigerated for up to 24 hours.

Using a countertop or immersion blender, process tomatoes until a coarse but evenly blended sauce forms, about 10 seconds. Transfer to a 2-cup liquid measuring cup; if needed, add reserved tomato liquid to yield 2 cups (475ml) sauce. Season to taste with salt and pepper and set aside.

Preheat pizza oven to 800°F (425°C). When ready to bake, coat one dough ball generously on both sides with flour and place on well-floured surface, seam side down. Gently press out dough into rough 8-inch circle, leaving outer 1-inch higher than the rest. Gently stretch dough into a 10- or 12-inch circle (final dimension depends upon the size of your oven) about ¼-inch thick by draping over knuckles and gently stretching. Transfer to floured wooden or perforated metal pizza peel.

Working quickly, spread an even layer of tomato sauce over pizza, leaving outer ½-inch rim untopped. Spread string cheese evenly over sauce, then dollop meat mixture over pizza in small chunks. Drizzle with olive oil.

Transfer pizza to oven and bake, rotating pie regularly with a metal peel for even cooking, until rim is lightly charred and bottom is crisp, 90 to 180 seconds total. Retrieve pizza with a metal peel and transfer to a cutting board. Sprinkle with parsley and sumac, slice, and serve immediately.

Repeat steps 5 through 7 for remaining pizzas.