Preheat oven to 400 °F. Pierce eggplant all over with fork. Put 2 tablespoons oil on cookie sheet. Add eggplant and turn to coat.
Bake until very tender, turning once, about 55 minutes. Cut in half lengthwise and let cool.
With a spoon, scrape flesh from eggplant into sieve. Drain 1 hour, pressing occasionally on eggplant with spoon.
Transfer to bowl. Mash with fork. In a small, heavy skillet over low fire, heat 1 tablespoon oil.
Saute onion and garlic until tender, about 6 minutes.
Add to eggplant. Mix in flour, then egg. Season with salt and pepper. (This maybe done 4 hours ahead. Cover and chill until ready to cook.)
Heat a tablespoon oil in large non-stick skillet over medium heat.
Drop eggplant mixture, about 2 tablespoons for each pancake, spacing evenly onto hot skillet.
Cook until golden about 5 minutes per side. Repeat with remaining eggplant mixture.