Place rice in a large colander and rinse with cold water until water runs clear. Let rice sit 15 minutes to drain completely. Place rice in a medium saucepot and cover with 2 cups cold water. Bring to a boil. Reduce heat to low, cover and simmer 15 minutes. Remove from heat and let stand, covered, 15 minutes.

Meanwhile, in a small saucepan heat 3 tablespoons vinegar to a simmer. Remove from heat and whisk in sugar and salt until dissolved. Place vinegar mixture and rice in a large bowl and toss to combine. Let cool completely.

In a medium bowl, toss cucumber, avocado, carrot and crabmeat until combined. Divide rice evenly between four serving bowls and top with cucumber mixture. In a small bowl, whisk together remaining 2 tablespoons rice vinegar and soy sauce. Drizzle over the top and garnish with pickled ginger and sesame seeds.