Position racks in the upper and lower thirds of the oven; preheat to 425 degrees F. Put each crust on a baking sheet. Brush each with 1 teaspoon olive oil. Divide the pizza sauce between the crusts and spread almost to the edges with the back of a spoon. Sprinkle with the mozzarella, parmesan and oregano. Scatter the artichokes evenly over the pizzas. Bake, switching the pans halfway through, until the crusts are crisp and the cheese browns slightly, 12 to 15 minutes.
Meanwhile, combine the escarole, mortadella, roasted pepper and giardiniera in a large bowl. Drizzle with the giardiniera brine and remaining 1 tablespoon olive oil and season with pepper. Toss.
Cut the pizzas into quarters and divide among plates. Serve with the salad.