You want the eggplant to be very shriveled up and look almost as though you ruined it, to the point of nearly falling apart. However, try to avoid breaking the skin (other than the fork pricks) because the skin helps to contain the mess and cook it evenly.
If putting it directly on the burner seems too messy you can also put it on a pan and set the oven to broil, which will accomplish nearly the same effect since it is using high direct heat. Another alternative is to bake in the oven until the eggplant shrivels. Either way, you will get a similar result.
If you don’t have a food processor, you can just mash it altogether leaving it chunky, which some people prefer. Blending it will give a smoother texture.
Baba Ghanoush is often served at room temperature, but should always be stored cold in the refrigerator. It will keep 2-3 days.