Preheat oven to 200ºC .
Prick eggplant with a fork in 10-12 places and rub with olive oil. Bake uncovered for about an hour, or until the pulp feels quite soft. Scoop out the pulp and place in a small saucepan. Add lemon juice and cook over medium heat until the water has evaporated about 5 minutes.
Saute the onion in butter. Blend enough of the flour in to make a thick roux, then add milk slowly to form a thick sauce. Beat lightly into the eggplant. Season with salt, pepper and nutmeg. Add the parmesan cheese and a few drops of warm milk if dip is too thick.
Store overnight in the refrigerator but bring to room temperature before serving with crackers, bagel chips, or strips of crisped pita.