Heat oven to 500 degrees F. Lightly oil 2 (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 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 Pizza Dough in half. Cover 1/2 with plastic wrap while working with the second. Working on a lightly floured surface, use fingers to flatten and stretch half the dough into a rough 8-inch circle. Transfer to 1 of the prepared pizza pans. Continue to press dough out until it fits just inside rim of pan. Dough should be less than 1/4-inch thick. Drizzle with olive oil. Repeat with second piece of dough.
Sprinkle each round with 1/2 of 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 cheese. Return to oven until crusty and golden, 10 to 15 minutes more. Serve immediately.
Measure the flour onto a clean work surface and make a well in the center. Dissolve the yeast in a bowl with 3/4 cup lukewarm water. Place the salt, yeast and olive oil in the well, and with the help of a fork, incorporate the flour into them. Add more lukewarm water as needed to make a dough that is homogeneous and elastic.
Dust a large bowl with flour. Place the dough in the bowl. Cover with plastic wrap and set it in a warm place to rise until doubled in size, about 2 hours.
Oil 2 (12-inch) pizza pans each with 2 tablespoons. On a lightly floured surface, knead dough until very smooth. Divide dough in half. Using a rolling pin, roll each half, 1 at a time. Transfer dough to prepared pans. Stretch dough with your hands to form rounds 1/4-inch thick.
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