Cook the sushi rice according to package directions, season it as desired, and let it cool slightly.
Prep the fillings by slicing the avocado and cucumber into thin strips.
Once the rice is cooled off but still warm, stir together the rice vinegar, sugar, and salt until the sugar is mostly dissolved. Gently fold the mixture into the cooked rice without mashing it.
Place one sheet of nori on your bamboo sushi mat with the shiny, smooth side facing DOWN and the rougher side facing UP. The rice goes onto the rough side, which helps it stick.
Spread a thin layer of rice evenly over the nori, leaving a small border at one edge. Wet your fingers as needed to keep the rice from sticking.
Add the tuna, avocado, and cucumber in a line across the center of the rice.
Roll the sushi tightly, using the mat or saran wrap to gently press and shape the roll as you go.
Slice with a sharp, damp knife into even pieces.
Finish with Everything But the Bagel seasoning and serve with your favorite dipping sauce.