Season the turkey with salt, pepper and herbs. Coat with olive oil, place in a baking pan and pour the chicken broth around the turkey. Place in the oven and bake for 30 to 40 minutes. Remove from oven and let cool in the baking pan for 10 minutes. Slice into 1/2-inch slices, on an angle. Allow to sit in baking pan with juices as you make sauce.
In the bowl of a food processor add the tuna, anchovy, lemon juice and capers. Puree until creamy, about 1 minute. Pour the tuna mixture into a bowl and stir in the mayonnaise.
Place the slices of turkey on a platter and pour the tuna sauce on top. Garnish with chopped parsley.