2) Wash and pat dry the tuna steaks. Season with salt and pepper and brush both sides with olive oil. Place tuna on hot griddle and sear each side for 2 minutes for rare. If you prefer well done, cook the tuna an additional 2 to 3 minutes per side. Remove and let rest.
3) Add the garlic, basil leaves, pine nuts, salt, and pepper into the bowl of a food processor. Pulse until finely chopped. With the blender still running, slowly pour in 125 ml of olive oil. Check for a thick, yet smooth consistency, adding more oil if necessary. Transfer to a bowl and stir in parmesan.
4) Slice the tuna across the grain and on a bias into 1 1/4 cm thick slices. Place the slices on a serving plate and drizzle with lemon juice. Spoon the pesto over the tuna and serve.