Cut the eggplant into 1/3 inch thick slices. Heat the grill and cook the eggplant slices until they are soft and lightly browned on both sides, about 8 minutes, turning once. Season the eggplant slices with salt.
Break the eggs in a large bowl. Whisk them mildly with salt. Grease a round 8 inch pie pan or baking dish with the butter. Pour in the egg mixture. Lay the grilled eggplant slices in the pan, they will sink slightly into the eggs. Sprinkle the sesame seeds over the eggs.
Bake for 20 minutes, or until the eggs are set and the top is lightly golden. Serve the frittata hot or at room temperature and cut into squares.