Rinse spinach and add to a pot of boiling water, cooking just until wilted, approx. 30-45 sec. Remove and run under cold water, squeezing water out. Add 1 teaspoon of sesame oil and pinch of salt to spinach. Set aside.
Heat nonstick skillet over medium-high with a few drops of sesame oil. Pour eggs into skillet and move around to form very thin sheet; once set enough to flip, carefully do so. Cook until just barely firm, but still golden on both sides. Transfer to cutting board and slice into long, thin strips.
In same skillet, heat 1 teaspoon sesame oil and sauté carrot just until soft. Remove from heat and set aside. Add remaining sesame oil and pinch of salt to rice, tossing to coat well; taste and adjust seasonings, as desired. Toss tofu with kimchi juices to season, to taste.
Gather spinach, carrots, egg, rice, tofu and radish kimchi, and place separately at top of work surface. Using a bamboo sushi rolling mat, place one sheet of nori in center of mat, shiny side down. Spread rice over two-thirds of seaweed in thin layer. Layer fillings in a generous 1-inch strip along center of rice. Starting with the side closest to you, tightly roll over filling, lifting bamboo mat with seaweed, and pressing along roll with each turn.
Continue in short quarter turns, pressing as you go, until completely rolled; add a few drops of water to exposed internal edge of nori to help it stick on last turn. Repeat with remaining rolls. Rub a few drops of sesame oil on outside of rolls. Slice into bite-size pieces. Serve with Kimbap Sauce.
Combine all ingredients and serve at room temp.