Drain the canned tuna thoroughly and place it in a medium mixing bowl.
In a small bowl, whisk together the avocado oil mayonnaise, sriracha, toasted sesame oil, rice vinegar, and coconut aminos until smooth.
Pour the dressing over the tuna and add the sea salt and black pepper, then mix well until the tuna is fully coated.
Lay the seaweed sheets flat on a clean cutting board or bamboo rolling mat.
Spread 0.5 cup of warm cooked brown rice evenly over the bottom two-thirds of each seaweed sheet, leaving the top edge clear.
Divide the spicy tuna mixture between the two sheets, layering it across the center of the rice.
Top the tuna with avocado slices, julienned cucumber, and shredded carrots.
Sprinkle with sliced green onions and sesame seeds.
Carefully roll the seaweed from the bottom up into a tight cylinder, lightly wetting the top edge with water to seal the wrap.
Slice each wrap in half with a sharp, damp knife and serve immediately.