To prepare the tapenade: Drain all but one tablespoon olive oil from the jar of Tonnino Tuna and then drain into the food processor container.
Add the anchovy paste, thyme, parsley, lemon peel and garlic and pulse several times. Add the lemon juice, 3 tablespoons olive oil and mascarpone and process until almost smooth.
Add the olives, capers and salt and pepper and pulse to mix.
Transfer the mixture into a container, cover with plastic wrap and refrigerate for at least 1 hour.
To prepare the crostini: Meanwhile, preheat the oven to 375° F. Brush one side of the bread lightly with olive oil. Arrange the bread on a baking pan and bake for 6-8 minutes. Allow to cool slightly.
Assembly: Spread the tapenade on each toast, sprinkle with parsley and serve.