This is an odd recipe, and I've never seen anything like it. It was published in a 1971 Time-Life books recipe series. It is either magically delicious, or nasty. I can't imagine a middle range. No, I'm not going to try it, but if you do, let me know.
Eggplant-Banana Casserole
1 medium eggplant, cut crosswise into 1/4 inch slices
2 teaspoons salt
1 tsp crumbled dried thyme
1/2 tsp black pepper
1/2 - 1 cup vegetable oil
Butter to grease the pan
4 tbsp butter, cut into 1/2-inch bits
3 large ripe bananas, peeled and cut lengthwise into halves
3/4 tsp ground nutmeg
3 large firm ripe tomatoes
Sprinkle the eggplant slices with salt and spread them out between paper towels and put a cookie sheet on top and let them rest 20 - 30 minutes. Season on both sides with thyme and pepper. Heat up a skillet with some oil and cook the eggplant on both sides, a minute or two per side, regulating the heat so they color quickly without burning. Transfer to paper towels while you cook all the slices, adding more oil as needed.
Meanwhile, preheat the oven to 350 degrees and butter a 1 1/2 quart baking dish at least 2 inches deep. Melt the 4 tbsp butter and fry the banana halves in it until golden brown. Remove from the pan and sprinkle with nutmeg.
Peel the tomatoes (use the dipping in hot water method) and slice into 1/4 inch slices. Season with salt.
Put about half the eggplant slices in the baking dish and arrange 3 banana halves side by side over them and cover with half the tomatoes. Repeat the layers with the rest of the eggplant, bananas, and tomatoes, and place two of the best-looking eggplant slices on top. Bake in the middle of the oven for 30 minutes, or until the top has begun to bubble. Serve at once. This makes 4 servings.