To make the mayonnaise: Beat the egg yolks in a mixing bowl. Then drizzle extra-virgin olive oil in a thin steady stream while continuously whisking the yolks. Add the salt, to taste, freshly squeezed lemon juice, and continue to whisk the mixture until well blended and creamy.
Cut off the top 1/3 part of each tomato. Then carefully scoop out and discard the inside of each tomato with a spoon.
To make the filling: Drain the oil from the tuna and place the tuna in a bowl. Then add the parsley. Chop 2 tablespoons capers and add to the mix. Add 3/4 of the mayonnaise. Mix well. Divide the tuna mixture among the tomato shells. Spoon the mixture into the tomato shells. Top with the remaining mayonnaise and capers.