Sliced eggplants lengthwise, about 1/2-inch thick. Sprinkle with 1/2 teaspoon salt. After 30 minutes, dab them dry.
Preheat oven to 400F.
Brush eggplant slices with 2 tablespoons olive oil and roast 15 minutes. Reduce oven temperature to 350F.
Heat 2 tablespoons olive oil in a skillet over medium heat. Add garlic and onions and sauté until translucent. Add diced tomatoes, nutmeg, remaining 1/2 teaspoon salt and pepper. Continue sautéing until ingredients meld into a chunky sauce.
Layer eggplant and sauce in a 13 x 9-inch baking dish. Top with cheese. Bake until sauce is thoroughly heated and cheese is browned and bubbly.