Peel eggplants in such a way that 3 strips of skin remain on each eggplant. Cut peeled eggplant into 1/2-inch slices. The strips of skin will prevent the eggplant slices from falling apart while cooking.
Bring vegetable broth to a boil in a large pot and cook eggplant slices for 1 minute. Pour into a sieve and drain well.
Preheat oven to 375 degrees F (190 degrees C). Grease a large baking dish with 1 tablespoon olive oil. Spread out eggplant slices on the bottom of the baking dish.
Heat remaining 2 tablespoons olive oil in a large skillet over medium heat and cook bell peppers, onions, and garlic until softened, 5 to 10 minutes. Season with salt and pepper and layer over eggplant. Add tomato slices; season with salt and pepper.
Bake in the preheated oven until vegetables are tender, 20 to 30 minutes.
