Drain all but a tablespoon of olive oil from the tuna and then flake the fish into the bowl of a food processor fitted with the steel blade. Add the anchovy paste, thyme, parsley, lemon zest, and garlic and pulse a few times. Add the lemon juice, 3 tablespoons of olive oil, and the mascarpone and process until almost smooth. Add the olives, capers, salt, and pepper and pulse just to incorporate. Transfer the mixture to a bowl, cover with plastic wrap, and refrigerate for at least 1 hour.

Meanwhile, heat a gas or charcoal grill or preheat the oven to 375 degrees. Brush the bread lightly on one side with olive oil. Grill the crostini on both sides until lightly browned or arrange the bread on a sheet pan and bake for 6 to 8 minutes. Allow to cool slightly.

Mound the tapenade on each toast, sprinkle with parsley, and serve.