Preheat the oven to 500˚ F. Line a large rimless baking sheet with parchment paper. Mix the pizza sauce, finely chopped scallions, pepperoncini, 2 tablespoons pomegranate molasses, cinnamon, allspice and 1/2 teaspoon each salt and pepper in a large bowl. Set aside 1/4 cup of the sauce mixture. Add the lamb to the bowl with the remaining sauce and mix well.
Rub the pizza dough with 1 tablespoon olive oil on the prepared baking sheet. Stretch into a large oval, about 11 by 15 inches. Prick the dough all over with a fork, then top with the meat mixture, pressing it into a thin, even layer up to the edges of the dough. Brush with the reserved sauce and sprinkle with the pine nuts.
Bake until the meat is cooked through and the dough is dark golden brown, 10 to 12 minutes. Let cool about 5 minutes; sprinkle with the sliced scallion greens.
Whisk the remaining 1 tablespoon each pomegranate molasses and olive oil with 2 teaspoons water in a medium bowl. Add the herbs and toss gently to coat. Cut into 8 pieces and serve with the herb salad.