Combine ½ cup Ponzu sauce with ¾ cup water and cook the rice according to the package directions. (Note: if you use an Instant Pot for making your rice, use only ½ cup water and add 1 tablespoon vegetable oil.)
Cut the tuna into ½-inch dice and toss with 2 tablespoons Ponzu sauce. Cover and refrigerate until serving.
Using a vegetable peeler, cut the cucumber in ribbons. Start on one side and slice until you reach the seeds, then turn and do the same on the other 3 sides. Discard the seeds. Pat dry with paper towels.
Cut the avocado in half, remove the pit, slice while still in the peel, then use a spoon to remove all the slices.
To assemble, make separate piles of the ingredients. Tuck in the pickled ginger and shallots. Sprinkle the nori over the rice and some sesame seeds over the tuna. Serve immediately with some Ponzu sauce for dipping.
Combine ¼ cup grenadine with ¼ cup Marukan rice vinegar in a small saucepan and bring to a boil. Turn off the heat, add 1 large shallot, thinly sliced, and let sit for 15-30 minutes. Drain.