Cut the eggplant in half lengthwise. Use a sharp paring knife and carefully trim around the inside edges, leaving a rim approximately ¼inch thick. Score the center flesh almost but not down to the skin.
Heat the oil in a skillet and place the eggplant halves, scored side down, in the oil. Cover with a tight-fitting lid or aluminum foil. Cook over low heat until the eggplant is tender, 15 to 20 minutes.
Preheat the oven to 350 degrees.
Using a large spoon, scoop out the eggplant flesh, leaving a shell. Chop the flesh.
Rinse the mushrooms and drain them. Slice the mushrooms, then chop them fine. There should be about 2cups.
Heat 2tablespoons butter in a skillet and add the mushrooms, the juice of ½ lemon, and salt and pepper to taste. Cook, stirring, until the mushrooms give up their liquid. Continue cooking until almost all the liquid evaporates.
Heat 2tablespoons butter in another skillet and add the onion. Cook, stirring, about 3 minutes, and add the celery and green pepper. Cook about 5 minutes and add this to the mushrooms.
Peel and devein the shrimp and chop them fine. Add them to the mushroom mixture. Add the chopped eggplant flesh, nutmeg, cayenne, salt and pepper to taste, and 1teaspoon lemon juice. Add ½cup bread crumbs, the heavy cream, and egg yolk. Fill the eggplant shells with the mixture. Sprinkle each half with equal parts of the remaining bread crumbs, and dot with equal amounts of the remaining butter. Place the shells in an oiled baking dish and bake25 minutes, or until piping hot and bubbling. Run the eggplant briefly under the broiler until nicely golden. Serve piping hot.