Prepare the brown rice according to package instructions and let it cool to room temperature.
Cut the sushi-grade ahi tuna into uniform 1/2-inch cubes using a sharp knife.
In a small mixing bowl, combine the tamari, sesame oil, rice vinegar, grated ginger, and lime juice to create the dressing.
Gently toss the tuna cubes in the dressing until well coated and refrigerate for 10 minutes to allow flavors to meld.
Thinly slice the cucumber into rounds and the avocado into wedges.
Divide the cooled brown rice into serving bowls.
Arrange the marinated tuna, edamame, cucumber slices, and avocado wedges over the rice.
Finish the dish by garnishing with toasted sesame seeds and thinly sliced green onions.