Season the tuna with salt and pepper and grill for about 3-4 minutes per side.
Put tuna in a dish and add olive oil and thinly sliced garlic, cover and refrigerate for at least 6 hours. Bring the potatoes to a boil in a large covered sauce pan, cook until tender (about 20 minutes) then drain and slice the potatoes.
In a large saucepan of boiling water, cook the beans for about three minutes (until crisp) and drain. Drain the tuna but keep 5 tablespoons of the oil and whisk it in a large bowl with the lemon juice and toss in minced garlic with the potatoes, beans, tomato, parsley, and salt and pepper.
Transfer to a large platter and slice the tuna and arrange over the vegetables. Garnish the plate with the egg and olives.