Rinse the sushi rice and cook according to the package instructions, using the amount of water recommended for your brand. Gently fold in the rice vinegar and let the rice cool until comfortable to handle.
Mix the drained tuna with the red onion, 3 tablespoons mayonnaise and Sriracha to taste. In another bowl, stir the remaining mayonnaise with the soy sauce.
Place a nori sheet on a piece of food wrap with one corner pointing toward you. Form a compact square of rice in the centre. Add tuna, avocado, cucumber, cream cheese, carrot and a little sauce, then top with another thin layer of rice. Divide the fillings across four burgers.
Fold the nori corners over the filling. If needed, use a second nori sheet to enclose any gaps. Wrap snugly in food wrap and let stand for 5–10 minutes so the nori softens and the layers hold together.
Unwrap and cut in half with a sharp knife, wiping it between cuts. Serve promptly or refrigerate. Total time is approximate and depends on your rice’s cooking and cooling time.