Sprinkle eggplant slices with 2 teaspoons salt; let stand 1 hour. Rinse eggplant well, and pat dry. Sprinkle eggplant with remaining 1/4 teaspoon salt and pepper; drizzle with oil. Let stand 15 minutes.
Place eggplant on a rack in a broiling pan. Broil 5 inches from heat 10 minutes on each side, basting with barbecue sauce the last 3 minutes.
Note: For testing purposes only, we used K.C. Masterpiece for barbecue sauce.