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1
Mix the basil, tapenade, capers, anchovy, and chile in a small bowl. Using a sharp paring knife, make an incision along 1 side of each tuna steak. Move the knife back and forth to make a pocket. Divide the stuffing into 3 equal parts and stuff the tuna steaks. Place the steaks in a shallow nonreactive baking dish.
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2
Mix the 1/3 cup of olive oil with 3 tablespoons of the lemon juice, oregano, rosemary, peppercorns, and garlic in a small bowl. Pour the marinade over the fish and marinate in the refrigerator for 4 hours.
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3
Using a paring knife, trim an artichoke of all external green leaves as well as the green exterior of the stem. Once the artichoke has been trimmed down to the tender, yellow-hued leaves, cut it in half. Using a mandoline or a very sharp knife, very thinly slice the artichoke. Transfer the slices to a bowl of cold water with the remaining 1 tablespoon of lemon juice. Repeat this process quickly with the remaining artichokes, making sure they do not turn brown.
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4
Preheat a grill or grill pan to medium-high heat. Remove the fish from the marinade and season with sea salt and pepper. Grill until the tuna is well seared but still medium-rare, about 3 minutes per side. Remove the tuna from the grill and cut it into 1-inch-thick slices.
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5
Transfer the tuna to a platter, drizzle with the remaining 2 tablespoon of olive oil and the balsamic vinegar. Garnish with the shaved cheese, parsley leaves, artichoke slices, lemon wedges, and halved olives, if desired.
