Slice the eggplant thinly. Sprinkle both sides with kosher salt and place into a strainer in the sink. Allow to sit for 20 to 30 minutes. Rinse eggplant lightly in cold water, then pat the slices dry between layers of paper towels.
Slice grape tomatoes in half lengthwise and toss into a bowl with minced garlic.
Slice mozzarella very thinly.
Cut eggplant slices into fourths, and toss with olive oil. Arrange on a baking sheet and place 8 inches under the broiler.
Broil for 3 minutes, then toss around and broil another 3 minutes. Remove pan from oven and add tomato/garlic mixture. Broil for 2 to 3 minutes, then remove and set aside. (May do this 1 hour in advance.)
Preheat oven to 500 degrees.
Drizzle olive oil on a large baking sheet and use fingers to coat thoroughly. Remove the pizza dough from the bowl. Stretch pizza dough into a large rectangle, pressing with fingers to finish forming. Dough will be very thin.
Lightly drizzle a little olive oil on the dough and use fingers to spread. Lay mozzarella slices over the surface of the dough. Spread vegetables all over the surface of the cheese. Top with Parmesan cheese.
Bake for 10 to 12 minutes, or until crust is golden brown and the cheese is bubbly. Remove from pan and slice with a pizza cutter. Serve immediately!