In a large bowl, combine the cooked sushi rice, rice vinegar, sugar, and salt. Mix well and let it cool to room temperature.

In a separate bowl, combine the drained tuna, diced avocado, cucumber, red bell pepper, and green onions. Gently fold in the soy sauce, sesame oil, and lime juice until everything is well combined.

Once the rice has cooled, form small rice cakes by pressing about 1/4 cup of rice into a mold or your hands. Heat a non-stick skillet over medium heat and add a little oil. Cook the rice cakes for about 3-4 minutes on each side until golden and crispy.

To serve, place the crispy rice cakes on a plate and top each with a generous scoop of the tuna and avocado mixture. Sprinkle with black sesame seeds and red pepper flakes if desired.