Meanwhile, cut the cucumbers in half lengthwise. Using a spoon, scoop out the seeds. Cut the cucumbers into 1/4-inch-thick slices crosswise (makes about 2 cups). Add the cucumbers, carrot, chile pepper, scallion and sesame seeds to the remaining marinade, and refrigerate until ready to serve.
Remove the fish to paper towels and discard the marinade in the dish. Pat the excess marinade from the tuna. With a pastry or barbecue brush, brush the fish with additional olive oil.
On an outdoor grill or a grill pan over high heat, lightly brush the grates with olive oil (do not place the fish on the grill until the flames have subsided). Grill the fish 3 to 5 minutes on both sides for medium rare or 6 to 8 minutes for medium well. When slightly cooled, cut into thick slices. Meanwhile, mix the lettuce and herbs with the chilled marinade and transfer to a platter. Place the fish on top, and drizzle additional marinade over the fish. Serve immediately.
Recommended variations: For beef, marinate 1 1/2 pounds of filet 1 to 2 hours. Grill 12 to 14 minutes, turning often, for medium rare. For tofu, cut 1 pound of tofu into 1/2-inch-thick slices and marinate for 1 hour. Pat dry, brush with oil, and grill 2 minutes per side. For eggplant, cut 1 large eggplant into 1/2-inch-thick slices and marinate for 1 hour. Pat dry, brush with oil, and grill 2 minutes per side.