Eggplant has a wonderful ability to become very tender and silky when roasted or braised. When paired with fresh tomatoes and basil, it can be sublime. This dish is a terrific way to use fresh vegetables from the garden, but it’s also hearty enough to serve as a wintertime side dish.
Heat oven to 400°. Arrange eggplant halves, cut sides up, in a 9x13-inch baking pan. Season each half with about teaspoon sprinkling of salt.
In a 12-inch skillet over medium-high heat, cook onions in oil until translucent, about 5 minutes. Transfer onions with oil to a medium-size bowl and stir in tomato, parsley, basil, sugar, and remaining salt. Spoon tomato mixture on top of eggplants. Pour broth into bottom of pan, cover with foil, and bake 15 minutes. Baste eggplants with liquid in pan; then re-cover and return to the oven for an additional 15 minutes. Baste again, discard foil, and bake until eggplants are tender, about 20 minutes more. Serve warm with a drizzle of sauce.