Preheat the oven to 450°F (230°C) and position a rack in the center. Brush a heavy baking sheet with about 2 teaspoons of the oil.

Cut the eggplant into 1/2-inch (1.4cm) rounds and set them on the prepared baking sheet. Brush the rounds with more oil and season them with salt and pepper. Bake until the eggplant is softened and golden on the side touching the pan, 12 to 15 minutes. Flip the slices, brush them lightly with oil, season with salt and pepper, and continue baking until they are tender all the way through, 5 to 8 minutes more. Remove from the oven.

While the eggplant is baking, heat 1 tablespoon of the remaining oil in a heavy saucepan over medium-high heat. Stir in the onions and when they start sizzling, reduce the heat to medium. Cook, stirring occasionally, until the onions are nearly translucent, about 8 minutes. Stir in the garlic and cook until it starts to turn translucent, 2 to 3 minutes. Add the tomatoes and the bay leaf, stir, season with salt and pepper, and bring to a boil. Cook, stirring regularly so the tomatoes don't stick, until the tomatoes are softened and beginning to form a sauce, about 20 minutes.

Coarsely chop the herbs.

Place the remaining oil in a heavy, 1 1/2-quart (1.5L) baking dish. Place one layer of eggplant on the bottom. Sprinkle with one-third of the chopped herbs, and pour over one-third of the tomato sauce. Repeat, and then sprinkle half the cheese on the tomato sauce. Top with the remaining slices of eggplant, basil, and tomato sauce, and the remaining cheese. Cover and bake until the dish is hot throughout and the eggplant and tomato sauce have married, about 20 minutes. Remove from the heat and let cool for at least 5 minutes before serving.