Slice eggplant into 1/2-inch slices. Salt the eggplant and let it sit for 15 to 20 minutes; rinse the slices and pat dry. Brush them with olive oil, sprinkle with thyme, and season with pepper. Place the slices on a baking sheet and roast, not turning, until brown and tender, about 30 minutes. Let cool.
Separate the dough into 4 rounds. Roll them out into 8 to 10-inch circles. Brush 2 of them with olive oil and lay half the eggplant in the middle of each. Top each with half the tomato sauce, some fresh oregano, half the mozzarella, and 1 tablespoon Parmesan. Top each with a round of dough and crimp the edges to make a seal (like a pie). Pierce the top crust to allow steam to vent, brush with olive oil, and sprinkle with remaining parmesan.
Position your oven racks to the upper most and lowest positions. Place 2 large baking sheets on the racks and preheat the oven to 375 degrees F. Carefully remove the sheets and dust them with cornmeal. Transfer the rounds to the baking sheets and brush each with some olive oil. Bake until the crusts are light brown on the bottom, about 20 minutes. When slightly cool, slice like a pie into 8 wedges.