Preheat oven to 425�Fahrenheit.
Combine the potatoes, 1 tablespoon of olive oil, the rosemary, 1/2 teaspoon of salt, and the black pepper in a baking dish, stirring to coat evenly. Roast for 15 minutes, then stir and add the onion. Continue roasting 20 minutes, shaking the pan every few minutes. Transfer to a large bowl and set aside.
Boil one inch of water in a saucepan fitted with a steamer basket. Steam the beans 5 minutes until tender-crisp. Drain, rinse with cold water, and drain again. Set aside.
Heat a gas grill or broiler. Lightly brush the grill rack or broiler pan with olive oil. Position the cooking rack about 6 inches away from the heat source.
Brush the tuna fillets with olive oil, sprinkling both sides with the remaining salt. Grill or broil 4 minutes on each side, until firm to the touch. Transfer to a plate and keep warm.
Combine the olives, garlic, anchovies, capers, thyme, lemon juice, remaining olive oil, potatoes, and beans in a large bowl. Mix well and divide among the plates, placing a tuna fillet on each. Garnish with the parsley.
