Rub half of the pesto on the tuna. Set aside for 15 minutes. Preheat the grill and the fryer. Place the potatoes in the fryer. Remove the excess pesto from the tuna, season and place it on the grill. Shake the potatoes. In a small bowl mix the remaining pesto and the butter. Turn the tuna. Remove the potatoes from the fryer and toss them in the butter and pesto mixture, season.. Top with the tuna. Garnish.