For the carrot, heat oil in a skillet over med-high heat. Cook carrots, adding 1 tablespoon of water to create steam. Cover with a lid and cook for 30 seconds. Continue to cook to soften the carrots, adding more water if needed. Season with a little bit of salt. Set aside to cool.
For the pickled radish, cut the strips in half lengthwise, the slice each strips into 1/4 thickness. Set aside.
For the spinach, season the blanched spinach with soy sauce. Toss well and set aside.
For the rice, season the rice with sesame oil, salt, and sesame seeds. Mix well.
To assemble; quarter the seaweed sheets so that you have total 20 mini sheets. Spread a tablespoon of rice even all over the seaweed with your fingers. (Dip the finger in the water if needed but not too often)
Top with carrot slices, spinach, and 1-2 strips of pickled radish. Roll it up tightly. Repeat the other sheets until you finish them all.
Brush the rolls with a little amount of sesame oil and sprinkle with toasted sesame seeds. Cut the rolls in half, if you prefer, and serve with dipping sauce.
To make the dipping sauce, combine all the ingredients and mix well.