Preheat oven to 450 degrees F. and very lightly grease a large baking sheet.

Cut smaller eggplant piece into 1/3-inch-thick slices. Spread eggplant slices in one layer on half of baking sheet and season with salt. Put remaining eggplant half and all but 2 tomato halves on second half of baking sheet. Roast vegetables in middle of oven 15 minutes or until eggplant slices are tender, and transfer eggplant slices to a plate. Roast remaining vegetables 15 minutes more, or until eggplant piece is very tender. Remove baking sheet from oven and cool vegetables slightly.

Scoop out flesh from eggplant piece into a food processor and puree with roasted tomatoes and unroasted tomato, vinegar, sugar, and salt to taste. Sauce and sliced eggplant may be made 1 day ahead and kept separately, covered and chilled.

On a work surface sprinkled with 1 teaspoon cornmeal, roll out 1 piece of dough into a 12 by 6 inch oval and transfer to a baking sheet. Repeat with remaining cornmeal and dough, ending up with 2 ovals on each of 2 baking sheets.

Increase temperature to 500 degrees F.

Spread sauce on dough ovals, leaving a 1/2 inch border around edge of each pizza. Arrange eggplant slices on sauce and sprinkle pizzas with basil and mozzarella.

Bake pizzas in lower and middle thirds of oven 15 minutes, or until crusts are crisp and pale golden.