All the amounts given (esp. the spices) are estimates. taste as you go and adjust to your taste
Roast the eggplant over an open flame or in very hot oven until it collapses or burns.
Set it aside to cool.
When cool, strip away the skin.
Chop the flesh.

Saute the onions in olive oil until starting to brown.
Add the garlic. saute another minute or so, then add the tomatoes.
Cook another couple of minutes, until the tomatoes start to break down a little.
Then add the eggplant, spices, and basil, and cook the whole thing until it starts to dry out a hair (maybe 5 min.)
Lastly, add tahini, salt and lemon juice. taste and adjust seasonings.
Serve warm with pita.
Drizzle a bit more olive oil over the top before serving.