Vegan Sushi Burger

Name: Vegan Sushi Burger
Ingredients: 1 Cup sushi rice, cooked; 1/4 Cup rice vinegar; 1 Tablespoon sugar; 1 Teaspoon salt; 1 Tablespoon coconut oil; 1 clove garlic, crushed; 1/3 Cup soy sauce; 1 Tablespoon mirin; 1 Tablespoon brown sugar; 1 Cup shiitake mushrooms, thinly sliced; 1/2 avocado; 1 Teaspoon wasabi; 1 Teaspoon vegan mayonnaise; 1 Teaspoon sriracha; Pickled ginger, to taste; Shredded red cabbage, to taste; Black sesame seeds, to garnish