Whisk up the anchovies and 3 tablespoons EVOO, poured slowly. Add the tomatoes, capers, olives, parsley, red onion, basil, garlic and red pepper flakes; stir and let stand for 30 minutes.
Heat a griddle or cast iron skillet over medium heat. Drizzle the fish with the remaining olive oil, about 1 tablespoon, and season with salt and pepper. Cook the fish for 2 minutes on each side for rare, up to 4 minutes on each side for more opaque fish.
Slice the tuna, then arrange on plates and top with lots of raw sauce.