Cook 1 cup of sushi rice with 1 1/2 cups of water in a rice cooker until tender.
In a bowl, mix the cooked rice with 3 tbsp rice vinegar, 1/2 tsp superfine sugar, and 2 tsp tamari sauce. Cover with a clean kitchen towel for 10 minutes.
For vegan sushi: Place a nori sheet on a sushi bamboo mat. Spread 1/4 cup of seasoned sushi rice over 3/4 of the nori. Arrange carrot, avocado, cucumber, and toasted tofu strips. Lightly brush the far end of the nori with water, then tuck and roll tightly using the mat. Gently press to shape, brush with sesame oil, and slice into 6 pieces.
For shrimp sushi: Place a nori sheet on a sushi bamboo mat. Spread 1/4 cup of seasoned sushi rice over 3/4 of the nori. Arrange carrot, avocado, cucumber, and 6 shrimp tempura. Lightly brush the far end of the nori with water, then tuck and roll tightly using the mat. Gently press to shape, brush with sesame oil, and slice into 6 pieces.
Sprinkle all sushi rolls with sesame seeds and serve immediately with extra tamari sauce for dipping.