Slice the sushi-grade Ahi tuna into long, thin strips approximately half an inch thick.
Cut the cucumber into thin matchsticks and slice the avocado into long wedges.
Place one nori sheet on a bamboo rolling mat and spread half of the cooked brown rice evenly over the bottom two-thirds of the sheet.
Arrange half of the tuna, cucumber, and avocado in a horizontal line across the center of the rice.
Drizzle the tuna lightly with toasted sesame oil and sprinkle with half of the sesame seeds and sliced scallions.
Roll the nori tightly from the bottom up using the mat, sealing the top edge with a drop of water.
Repeat the process for the second roll using the remaining ingredients.
In a small bowl, whisk together the coconut aminos, rice vinegar, grated ginger, and lime juice to create the dipping sauce.
Slice each roll into six even pieces using a sharp, damp knife and serve immediately.