Wash eggplant and drop without peeling into the water with salt.
Bring water to a boil, cover pot, and cook rapidly for 30 minutes.
Remove eggplant from pot, peel, and mash with a fork.
Add grated cheese, egg, and 1/2 cup butter.
Mix well and put mixture into a greased glass baking dish (1 quart).
Sprinkle with cracker crumbs and dot with remaining butter.
Bake in preheated moderate oven (375° F.) for 30 minutes.