Grill eggplant steaks indoors in a pan, or outdoors: Place on grates over moderate heat, 2 to 4 minutes per side.
Cut 2 1 1/4-inch-thick slices lengthwise from center of each eggplant; reserve curved ends for another use. Brush eggplant slices with grapeseed oil; sprinkle evenly with paprika, salt, and pepper, pressing to adhere.
Heat a grill pan over high heat. Grill eggplant steaks until charred and tender, 4 to 5 minutes per side. Remove from heat.
Pulse tomatoes and olives in a mini food processor until finely chopped. Transfer to a bowl. Stir in olive oil and vinegar.
Place 1 eggplant steak on each of 4 plates. Top eggplant with tapenade. Sprinkle with basil.