Rinse the tuna steaks and pat them dry with paper towels.
In a small bowl, combine 1/2 teaspoon salt and 1/2 teaspoon ground pepper.
Rub the salt-and-pepper mixture evenly over both sides of the tuna steaks, then brush each slice with the extra virgin olive oil. Let rest for 15 minutes.
While the tuna rests, toast the sesame seeds in a small dry saucepan over medium heat, stirring, until golden and fragrant, about 3 minutes. Transfer to a bowl to cool.
In a medium bowl, combine the julienned cucumbers, the remaining 1/4 teaspoon salt, the remaining 1/4 teaspoon ground pepper, 1½ tablespoons of the toasted sesame seeds, and the sesame oil; toss to coat.
Preheat a griddle or barbecue grill to medium-high. Cook the tuna steaks 5–6 minutes per side, or until cooked to your desired doneness, using tongs or a spatula to flip once.
Sprinkle the remaining 1/2 tablespoon toasted sesame seeds over the cooked tuna.
Cut each tuna steak in half and serve immediately with the cucumber sesame salad.