Make your base rice by stirring together cooked rice, 1 teaspoon of sesame oil, 1/2 teaspoon of salt, and 1/2 teaspoon of cracked black pepper. Set aside.
Prepare your spinach by adding it to a large pot of boiling water. Cook until the leaves turn bright green (about 1 minute) and remove from heat. Drain and rinse with cold water to prevent the spinach from getting too soggy. Squeeze out as much excess water as possible. In a small bowl, mix together spinach, 1/2 tablespoon sesame oil, 1/2 teaspoon salt, and 1/2 teaspoon black pepper. Set aside.
Prepare your Korean omelet or Gyerranmari by adding 1/2 tablespoon of extra virgin olive oil to a medium non-stick pan over medium heat. Pour your liquid egg replacer into your pan, sprinkle with a little salt and pepper, and let it cook for about 3 minutes, until a spatula easily loosens the "egg" from the bottom of the pan (if it doesn't come off easily, you need to cook it longer or you don't have a real non-stick pan). Flip the egg like a crepe and cook for another 2 minutes, until both sides are evenly cooked. Remove from heat and let it cool. Cut into 1/2-inch wide strips or julienne.
Prepare your carrots by adding 1/2 tablespoons of olive oil to a large sauté pan over medium-high heat. When the oil begins to shimmer (about 1 minute), add your carrots to the pan. Sauté for about 2 minutes, until the carrots begin to soften. Season with salt and pepper and finish with 1/2 tablespoon of sesame oil before removing from heat. Set aside.
Prepare your cabbage by adding 1/2 tablespoon of olive oil to a large sauté pan over medium-high heat. When the oil begins to shimmer (about 1 minute), add your cabbage to the pan. Sauté for about 2 minutes, until the cabbage begins to soften. Season with salt and pepper and finish with 1/2 tablespoon of sesame oil before removing from heat. Set aside.
Prepare your vermicelli by adding 1/2 tablespoons of olive oil to a sauté pan over medium-high heat. When it begins to shimmer (about 1 minute), add your cooked noodles, together with soy sauce and brown rice syrup. Toss and sauté for about 1 minute, until all the liquid has been absorbed by the noodles, and remove from heat. Set aside.
Prepare your tofu by slicing your cutlet into 1/2-inch thick pieces, lengthwise (so that you have thinner cutlets). Place them in a small, shallow container, and spoon beet juice over them, making sure that their surfaces are exposed to some beet juice. Place in the refrigerator for at least 30 minutes.
When the tofu is ready, add 1/2 tablespoon olive oil to a small non-stick pan over medium-high heat. When the oil shimmers (about 1 minute), add your tofu cutlets to the pan and cook for about 2 minutes, until the bright pink color gets a little dark and "baked" into the tofu. Flip the tofu and cook for another 2 minutes, until both sides are evenly cooked. Allow the tofu to cool, before julienning them. Set aside.
To assemble, slice one seaweed sheet in half. Attach that half to one full sheet by smearing a few rice kernels onto the top of one and pasting the two sheets together, forming one extra long seaweed sheet. Place the extra long sheet on a flat work surface (not a bamboo mat), and cover the entirety of the extra long sheet with approximately 1 cup of base rice. Next, place a standard sized seaweed sheet on top of the rice, positioned approximately 1/2-inch off the bottom.
Next, add approximately 1/2-inch thick rows of the following in this order: Gyerranmari, Spinach, Carrots, Cabbage, Daikon Radish, Pink Tofu, Vermicelli, Burdock Root.
Starting at the bottom, roll your sheet up and forward (away from you), making sure to use your fingers to tuck in any filling ingredients that try to escape. Gently squeeze the roll as you keep rolling forward, until the entire sheet is rolled. Repeat with remaining ingredients.
Brush the rolls with a little sesame oil before slicing into 1/2-inch thick pieces and serving immediately.