Drain 1 can tomatoes in a colander over a bowl, reserving 1/2 cup liquid. Drain remaining 1 can tomatoes; discard liquid. Combine tomatoes, reserved 1/2 cup liquid, and chickpeas in a bowl.
Heat 1 tablespoon oil in a large skillet over medium-high. Add garlic, 1/2 teaspoon salt, and next 5 ingredients (through eggplant); sauté 7 to 8 minutes or until slightly tender. Stir in tomato mixture and remaining 1/2 teaspoon salt; cover, and cook 5 minutes.
Uncover pan; stir in vinegar, paprika, and black pepper. Cook 5 minutes or until vegetable mixture is slightly thickened. Divide vegetable mixture among 4 shallow bowls; drizzle servings evenly with remaining 1 1/2 teaspoons oil. Sprinkle with basil leaves, if desired.