Preheat oven to 400°.
To prepare crust, lightly spoon flour into a dry measuring cup; level with a knife. Combine flour and next 4 ingredients (flour through 1/4 teaspoon salt) in a large bowl, stirring with a whisk; make a well in center of mixture. Add water and 1 tablespoon oil, stirring to form a soft dough. Turn dough out onto a lightly floured surface; knead lightly 4 times. Gently press dough into a 4-inch circle on plastic wrap; cover and chill 15 minutes.
Slightly overlap 2 sheets of plastic wrap on a slightly damp surface. Unwrap dough, and place chilled dough on plastic wrap. Cover with 2 additional sheets of overlapping plastic wrap. Roll dough, still covered, into an 11-inch circle. Remove top sheets of plastic wrap. Fit dough, plastic-wrap side up, into a 10-inch round removable-bottom tart pan coated with cooking spray. Remove remaining plastic wrap. Press dough against bottom and sides of pan. Pierce bottom and sides of dough with a fork; bake at 400° for 10 minutes. Cool completely on a wire rack.
To prepare filling, arrange eggplant on several layers of heavy-duty paper towels. Sprinkle eggplant with 1/2 teaspoon salt; let stand 15 minutes. Pat dry with paper towels; brush eggplant with 1/2 teaspoon oil. Arrange eggplant in a single layer on a baking sheet coated with cooking spray. Bake at 400° for 20 minutes. Stack eggplant slices on a plate; cover with plastic wrap. Let eggplant stand 7 minutes to steam.
Heat a large nonstick skillet coated with cooking spray over medium heat. Add garlic; cook 1 minute, stirring constantly. Remove from heat; stir in 1/4 teaspoon salt, basil, oregano, mint, and tomatoes.
Sprinkle 2 tablespoons smoked mozzarella on bottom of baked crust. Layer eggplant and tomato mixture in crust; sprinkle with 6 tablespoons smoked mozzarella and Parmesan. Bake at 400° for 10 minutes or until cheese melts. Cut into 8 wedges.