Preheat the broiler. Remove tuna from marinade and discard any excess liquid. Rub the tablespoons of olive oil on tuna and place on a non-stick baking sheet. Broil for 2 minutes, turn and repeat. Remove and cool, then refrigerate.
When very cold, slice into thin slices. Place slices on a platter overlapping just slightly. Drizzle with remaining teaspoon olive oil and remaining tablespoon lemon juice. Top with capers and parsley leaves. Serve very cold with 2 slices of baguette.