Put water and rice in a pot and bring to a boil. Cook over medium heat for 15 minutes, then set the rice aside and let it cool down.
Meanwhile, prepare the vegetables: cut the cucumber, carrot and pepper into strips.
Put a sheet of nori seaweed on the base, with the rough side up, spread the rice over the entire surface with wet hands (leaving the outer edge empty, 1-2 cm), then add the vegetables. Place the vegetables on the rice about three centimeters from the edge of the seaweed (on the first third).
Roll it towards the top, and make sure that the sushi is tightly wrapped.
Cut the sushi roll into small rolls and serve with soy sauce and wasabi.