Split the eggplant lengthwise; brush them with 1 T of the olive oil. Place the eggplant cut-side down on a sheetpan and roast at 450°F for 20-30 minutes or until the eggplant is very soft. Allow the eggplant to cool to room temperature.
When they are at room temperature scoop out the flesh of the eggplant with a spoon and discard the skins. Place the flesh of the eggplant in a colander to drain for about 20 minutes.
Place the drained eggplant in a food processor along with the lemon juice, tahini, garlic, salt, cayenne pepper, ground cumin and the remaining tablespoon of olive oil. Puree until the mixture is smooth and thick. Refrigerate at least 1 hour before serving.