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Preheat the oven with a pizza stone on a lower rack to 500 degrees F.
For the clams: Combine the clams, wine, shallots and garlic in a medium pan. Cook over high heat until the clams pop open, 3 minutes. Drain the clams in a colander set over a bowl to catch the liquid. Pick the meat from the clams, placing the meat in a small bowl. Strain the reserved juice over the clams.
For the pizza: Pulse the tomatoes and salt together in a food processor to a chunky consistency. Remove the dough from the bowl, keeping it as round as possible, and coat it completely with 00 flour. Stretch into a 12-inch circle, and transfer to a pizza peel.
Top the pizza with the tomato sauce, garlic, parsley, clams (without juice), chili oil, soppressata and pecorino cheese. Bake for 6 minutes.