Preparation Heat 1/4 cup oil in heavy large nonstick skillet over medium-high heat. Working in batches, add eggplant to oil and sauté until light brown, turning once and adding up to 2 tablespoons more oil as necessary, about 1 minute per side. Transfer eggplant to paper-towel-lined plate to drain. Sprinkle with salt and pepper. Cook tomatoes in boiling water for 1 1/2 minutes. Peel, seed, and chop into 1/2-inch pieces. Heat 1 tablespoon olive oil in heavy small saucepan over medium-high heat. Add onion, carrot, and half of garlic; sauté 5 minutes. Add tomato, thyme, 2 tablespoons water, and bay leaf; reduce heat to low and simmer until slightly thickened, about 15 minutes. Discard bay leaf. Season tomato mixture to taste with salt and pepper. Place basil, 3 tablespoons oil, pine nuts, 1 tablespoon Parmesan cheese, and remaining half of garlic in processor; puree. Set pesto aside. Preheat oven to 350°F. Place 4 individual gratin dishes (about 7x4 3/4 inches) on rimmed baking sheet. Place 2 slices eggplant in 1 prepared dish. Top with 1/4 of tomato mixture, 3 slices mozzarella cheese, 2 tablespoons pesto, and 1/4 cup Parmesan cheese. Repeat layering of remaining ingredients in 3 gratin dishes. Bake until heated through, about 8 minutes. Preheat broiler. Broil until cheese bubbles, about 3 minutes. Serve hot.
Preparation Heat 1/4 cup oil in heavy large nonstick skillet over medium-high heat. Working in batches, add eggplant to oil and sauté until light brown, turning once and adding up to 2 tablespoons more oil as necessary, about 1 minute per side. Transfer eggplant to paper-towel-lined plate to drain. Sprinkle with salt and pepper. Cook tomatoes in boiling water for 1 1/2 minutes. Peel, seed, and chop into 1/2-inch pieces. Heat 1 tablespoon olive oil in heavy small saucepan over medium-high heat. Add onion, carrot, and half of garlic; sauté 5 minutes. Add tomato, thyme, 2 tablespoons water, and bay leaf; reduce heat to low and simmer until slightly thickened, about 15 minutes. Discard bay leaf. Season tomato mixture to taste with salt and pepper. Place basil, 3 tablespoons oil, pine nuts, 1 tablespoon Parmesan cheese, and remaining half of garlic in processor; puree. Set pesto aside. Preheat oven to 350°F. Place 4 individual gratin dishes (about 7x4 3/4 inches) on rimmed baking sheet. Place 2 slices eggplant in 1 prepared dish. Top with 1/4 of tomato mixture, 3 slices mozzarella cheese, 2 tablespoons pesto, and 1/4 cup Parmesan cheese. Repeat layering of remaining ingredients in 3 gratin dishes. Bake until heated through, about 8 minutes. Preheat broiler. Broil until cheese bubbles, about 3 minutes. Serve hot.