Wash the rice with cold water until the water runs clear. Add the rice and water to the rice cooker and cook according to the instructions. Once cooked, transfer the hot rice to a large bowl and let it cool slightly. While still warm, fold in the sushi vinegar (or the mixture of rice vinegar, sugar, and salt).
Slice the sashimi-grade tuna into ½-inch thick strips.
In a small bowl, whisk together the mayonnaise and sriracha sauce. Taste and adjust the sriracha to your preferred heat level.
Add the tuna strips to the spicy mayo bowl. Gently toss to coat. Set aside.
Lay the bamboo mat with an optional piece of plastic wrap on top (This will make clean up easier).
Cut off 1/3 of the nori sheet using kitchen scissors.
Place the remaining nori sheet towards the bottom of the mat, shiny side down.
Take 3/4 cup of cooked rice and evenly spread over nori. You can wet your fingers in the tezu vinegar water* to prevent sticking)
Sprinkle with sesame seeds evenly on top. (I recommend toasting the sesame seeds first. Simply add the to a dry skillet on medium heat. Spread them evenly in the skillet and cook for about 5 minutes until lightly browned.)
Flip the rice-covered nori sheet so the rice side faces down on the mat.
Place tuna strips and sliced avocado on top of the nori.
Place your thumbs underneath the bamboo mat and lift the bottom edge up and over the filling. Roll forward firmly, applying gentle but even pressure throughout. Pull the mat back as you roll until the ends meet.
Once the roll is closed, press the mat firmly around it to shape into a tight, even cylinder.
Transfer the roll to a cutting board. Using a very sharp knife, cut the roll in half, then cut each half into 4 pieces for 8 pieces per roll. Wipe the blade with a damp cloth between each cut to keep the rice from tearing.
Serve immediately with soy sauce, pickled ginger, and wasabi paste.