Bring a pot of water to a boil. Prepare an ice bath in the meantime. Add the spinach to the boiling water and cook for 30 seconds. Remove the spinach, drain, and submerge in the ice bath. Once cooled enough to handle by your hands, squeeze as much water from the spinach as possible, and place it in a bowl. Add the garlic, salt, and sesame oil and toss to mix well. Set aside.

Heat the oil in a pan over medium heat until hot. Add the shredded carrot and salt. Cook and stir the carrots until they are wilted, 2 to 3 minutes. Transfer to a plate and set aside to cool.

Beat the eggs and salt together in a small bowl. Heat a medium-sized non-stick skillet over medium-low heat and spray (or brush) with a thin layer of oil. Add the egg, do not stir, and cover briefly. Once the egg is mostly set, about 1 to 2 minutes, flip it and cook for another 30 seconds. Remove the egg to a cutting board and slice into 3/4” (2 cm) strips.

Prepare a small bowl of water. Wear food gloves if available, to help prevent rice sticking to your hands. Cover your rolling mat with a piece of plastic wrap, and use a knife to slit a few lines on the mat. Lay one sheet of seaweed, rough side up and indented lines perpendicular to you, on a rolling mat (or on your work surface if not using a mat). Dip your fingers in the dish of water and pick up about 1 cup of rice, and place in the center of the seaweed sheet. Dip your fingers in the water again and spread the rice evenly across the sheet, leaving 1 1/2” (4 cm) of sheet uncovered at the top. For the best result, aim for the rice to be about two grains tall.

About 1”(2.5 cm) from the base of the seaweed, start to add the fillings onto the rice. Begin with two strips of egg and one strip of danmuji next to each other. Lay 1 to 2 slices of cucumber on top of the egg, and a layer of spinach on top of the danmuji. On top of everything add the carrots. Lift the base of the seaweed and roll it over the filling, squeezing and pressing from the center out to the edges. Continue rolling until all the rice is rolled, then brush some water along the edge of the seaweed sheet that’s not covered by the rice until it feels sticky and moist. Continue rolling over the wet edge then press down gently to seal. Set aside. Repeat with remaining ingredients.

Brush the top of the rolls with a thin layer of sesame oil and sprinkle with sesame seeds. Slice each roll into 10 pieces and serve at room temperature.