Scrub your vegetables thoroughly to remove any dirt or impurities.
After cleaning your vegetables, rough chop the potato, leek, onion, scallion whites, and carrot into large hunks. Cut the garlic cloves in half. Peel the radish so that you have 2 to 3 6-inch by 1-inch strips. Then, add sesame oil to a large stock pot or Dutch oven over medium-low heat, together with the rough chopped vegetables, garlic cloves, radish peel, salt and pepper. Sauté for about 2 minutes until the vegetables begin to brown. Add 8 cups of filtered water, together with dried mushrooms and kelp. Use a wooden spoon to scrape up any brown bits from the bottom of your pot and incorporate into your liquid.
Increase your heat to high and bring the contents of your pot to a boil (about 5 to 7 minutes). Then, reduce your heat to medium-low and simmer your liquid for about 45 to 60 minutes, until the amount of liquid has visibly reduced by about 25%.
Strain your liquid through a mesh strainer or a chinois into a large container (I used an 8 cup liquid measuring glass). You should end up with roughly 6 cups of Korean vegetable broth.
If you are using frozen rice cakes, thaw them in the refrigerator overnight or stick them in the microwave for about 1 to 2 minutes, until they are no longer frozen together. Add your rice cakes to a large bowl, pulling apart any large chunks of stuck-together rice cakes. Add 1 tablespoon of toasted sesame oil, 1 teaspoon of salt, and 1 teaspoon of black pepper. Stir the bowl of rice cakes until they are all evenly coated. Set aside.
To a large Dutch oven over medium-high heat, add 1 tablespoon of extra virgin olive oil and 1 tablespoon of toasted sesame oil. When it begins to shimmer (about 1 minute), add the scallion whites and julienned onion, together with 1 teaspoon of salt and 1 teaspoon pepper. Sauté for about 2 to 3 minutes, until the onion begins to grow translucent. Then, add your potatoes and sauté for an additional 2 minutes, until the potatoes start to get soft. Finally, add your marinated rice cakes to the pot and stir until the rice cakes are evenly coated and incorporated into your veggies.
Add the vegetable broth to your sautéed vegetables, using a wooden spoon to scrape up any brown bits on the bottom of your pan. Bring the contents of the pot to a boil and then reduce heat to medium-low and simmer for about 10 minutes, until potatoes are almost cooked (about 10 minutes).
While your soup is cooking, scramble your JUST Egg by adding a ½ tablespoon of extra virgin olive oil to a non-stick pan over medium heat, together with the JUST egg and a pinch of both salt and pepper. Stir the contents with a wooden spoon or chopsticks until they start to cook (about 2 minutes). Scrape the scrambled eggs into a small bowl and set aside.
When your potatoes are almost cooked, add your scrambled eggs along with frozen dumplings (they don't need to be thawed). Cook for an additional 2 to 3 minutes, until your dumplings are fully cooked. Season with additional salt and pepper, to taste.
To serve your vegan rice cake soup, apportion the soup into large bowls. Garnish with scallion greens, toasted sesame seeds, ribboned roasted seaweed, a drizzle of sesame oil, and fresh cracked pepper.
