Chill a serving dish in the refrigerator for at least 30 minutes.

Trim any dark flesh and fat from the tuna and discard.

Dice the tuna into 1/4-inch cubes.

Place the diced tuna in a large bowl.

Add diced cucumber, finely chopped scallions, 2 tablespoons of lime juice, soy sauce, 3 teaspoons of sesame seeds, grated fresh ginger, and sesame oil to the bowl.

Gently stir to combine all ingredients.

Season with salt, togarashi or pepper, and remaining 1 tablespoon lime juice as desired.

Transfer the poke to the chilled serving dish.

Sprinkle with the remaining 1 teaspoon sesame seeds.

Serve immediately with wonton crisps.