Rinse the sushi rice under cold water until the water runs clear. Combine the rinsed rice and water in a rice cooker and cook according to the rice cooker's instructions. Alternatively, bring a pot to the boil, then reduce heat to low, cover, and simmer for about 18 minutes.

Once the rice is cooked, transfer it to a large bowl.

In a small bowl, mix the soy sauce, mirin, sake, sugar, and honey (or maple syrup)

Heat vegetable oil in a pan over medium heat. Place the salmon fillet in the pan and cook for 3-4 minutes on each side, until it is almost cooked through.

Pour the teriyaki sauce mixture into the pan with the salmon. Let it simmer and reduce until it becomes slightly thick and coats the salmon. If you prefer a thicker sauce, add the cornstarch slurry and cook for an additional 1-2 minutes.

Place a bamboo sushi rolling mat on a clean surface and lay a sheet of nori on top, shiny side down.

With wet fingers, spread a thin, even layer of sushi rice over the nori, leaving a 1-inch (2.5 cm) border at the top.

Lay a few slices of teriyaki salmon, cucumber, and avocado along the center of the rice.

Roll the sushi tightly from the bottom edge using the bamboo mat, pressing gently to secure the roll. Once rolled, moisten the top border with a little water to seal the roll.

Use a sharp knife to slice the sushi roll into bite-sized pieces. Wipe the knife with a damp cloth between cuts for clean slices.

Serve the Teriyaki Salmon Sushi with soy sauce, pickled ginger, and wasabi.