Prepare a hot charcoal fire or preheat a gas grill (medium-high). When the fire is hot, distribute the wood chips if you are using them. Position the grill rack about 6 inches above the heat.
Lightly brush the eggplant and tomato slices on all sides with the oil. Lay the vegetables on the rack. Cover and grill, turning the vegetables once, until the eggplant is well browned and tomatoes are lightly browned and very tender, about 10 minutes total. Remove from the grill and cool to room temperature.
Roughly chop the eggplant and tomato. In a food processor, combine the chopped vegetables, tahini, lemon juice, garlic, soy sauce, salt, sesame oil and Tabasco and process until almost smooth. Transfer to a bowl, cover and let stand at room temperature for 1 hour. (Or, cover tightly and refrigerate overnight or for up to 3 days. Return to room temperature if chilled.)
Stir in the parsley. Adjust the seasoning. Spoon the eggplant mixture into the center of a platter. Sprinkle evenly with cumin or smoked paprika. Serve at room temperature.
Note: Though the smoky accent of the grill makes this spread particularly delicious, the vegetables can also be roasted in the oven. Preheat it to 450F, brush the eggplant slices and tomatoes with oil and roast until browned and tender, 20 to 25 minutes. Cool and then proceed with the recipe.