Mix the cooked brown rice, grated carrots, chopped bell peppers, and chopped cucumber together in a bowl.
Heat the sesame oil in a skillet over medium heat until it is hot.
Add the vegetable mixture to the skillet and cook for 5 minutes, stirring occasionally.
Add the soy sauce and stir to coat all of the vegetables with it.
Lay one sheet of Nori on a flat surface and spread half of the vegetable mixture onto it. Roll up the Nori into a roll. Repeat with second sheet of Nori.