This recipe was brought to us by chef and restaurateur Pino Luongo.
Preheat oven to 500 degrees. Lightly oil two 14-inch pizza pans. Set aside. In a medium skillet, heat 1/4 cup oil over high heat. Add artichokes, and cook, stirring, for about 1 minute. Add shallot, and cook, stirring, 1 minute more. Add wine and 1/2 cup water; bring to a boil. Cover, and lower heat to simmer. Cook until artichokes are tender when pierced with the tip of a knife, 8 to 9 minutes. Add marjoram, and stir to combine. Season with salt and pepper. Set aside.
Divide dough in half. Cover one half with plastic wrap while working with the other. Working on a lightly floured surface, use fingers to flatten and stretch dough into a rough 8-inch circle. Transfer to one of the prepared pans or onto a pizza peel. Continue pressing dough outward until it just fits inside rim of pan or reaches almost to the edge of the stone. Dough should be less than 1/4 inch thick. Drizzle with olive oil. Repeat with remaining dough.
Sprinkle each round with half the mozzarella. Transfer to oven, and bake for 10 minutes. Remove from oven. Divide artichokes evenly between pizzas, and sprinkle each with 2 tablespoons Parmesan. Return to oven until crusty and golden, 10 to 15 minutes more. Serve immediately.