Spread black olive paste on the rolls and top each burger with leaf lettuce and sliced red onion. Serve the green bean salad alongside.
Place an inch of water in a skillet and bring to a boil.
Place tuna in food processor and coarsely chop, then remove and transfer to a bowl. Add herbs and half of the lemon zest, season with salt and pepper, and combine. Form 4 large patties and reserve on a plate in the refrigerator until ready to cook.
Wash the food processor bowl and return to base. Place olives, capers, anchovies, remaining lemon zest and a drizzle of EVOO in the processor and process into a smooth paste.
To the boiling water, add some salt and the green beans. Cook 5 minutes, then cold-shock the beans under cold, running water. Drain and reserve.