Bake the garlic bread according to package instructions; keep warm.
Meanwhile, in a large, heavy skillet, heat the olive oil over medium-high heat. Add the onion and cook for 5 minutes. Add the eggplant and cook, stirring occasionally, until almost tender, about 7 minutes. Stir in the mushrooms and cook until they release their liquid and begin to brown, about 5 minutes; season with salt and pepper.
Stir in the white wine and cook, scraping up any browned bits, until the liquid has evaporated, about 2 minutes. Add the oregano and the tomatoes with their juices and simmer until slightly thickened, about 5 minutes.
Preheat the broiler. Halve the garlic bread crosswise. Divide the eggplant mixture among the 4 pieces and top with the provolone. Broil until the cheese is melted.