Preheat the oven to 425 degrees F. Line the bottom side of 2 baking sheets with parchment paper.
Mix together the capicola, pepperoncini and tomatoes in a medium bowl; season with salt.
Unroll 1 tube of the dough on a work surface and gently stretch into an 11-by-16-inch rectangle. Transfer to one of the prepared baking sheets. Repeat with the remaining tube of dough.
Brush each piece of dough generously with olive oil and sprinkle both the mozzarella and feta cheeses evenly on top. Scatter the tomato mixture evenly over each crust, holding back any juices so the crusts will not get soggy. Bake until the bottom of each pizza is brown and crust is crisp, 15 to 18 minutes. Sprinkle the oregano and crushed red pepper over the pizzas and serve.
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