Rinse the rice to remove excess starch. Combine the rice with the 3 cups of water in a saucepan and bring to a boil. Cover and let simmer for 10-12 minutes or until all the water has been absorbed. Remove from heat and leave covered for 10 minutes.
Transfer the cooked rice into a large bowl, add rice vinegar, and stir to combine. Set aside to cool completely.
In a medium bowl, add the cucumber, apple cider vinegar, and sesame oil and mix to coat evenly. Set aside to marinate for 10 minutes.
Place one nori sheet, shiny side down, on a clean sushi mat. Gently press 3/4 of a cup of the cooked rice in an even, ¼-inch layer, leaving ½ an inch on the sides.
Top with the avocado slices and marinated cucumber strips across the center of the rice and top with the microgreens.
Lift one edge of the nori sheet with the mat and fold. Gently but tightly roll once more and secure. Continue with the remaining nori sheets.
Use a very sharp knife to cut each roll into 1-inch pieces. Line the rolls in a single layer on a plate.
Sprinkle with the toasted sesame seeds and serve with soy sauce or tamari.