Preheat your grill to medium-high.
In a bowl, combine the tuna, the kalamata olives, and the scallions. Place the mixture in the freezer for 5 minutes.
1 lb. fresh tuna, 12 kalamata olives, 2 scallions
When the 5 minutes is up, transfer the tuna mixture into a food processor and pulse until the tuna is finely chopped.
Transfer back to the bowl and season to taste.
Sea salt and freshly ground black pepper
Flatten the tuna into 4 patties of equal size.
Brush each patty with olive oil and grill for 6 to 8 minutes total, flipping once.
Extra-virgin olive oil for brushing
In a small bowl, combine the mayonnaise with the anchovy paste.
¼ cup homemade mayonnaise, 1 tsp. anchovy paste
Spread the mayonnaise and anchovy paste on each tuna patty. Top with tomato and arugula, and serve.
Sliced tomatoes and arugula