ROAST THE SOY BEANS. Wash the beans 3-4 times in fresh water. You are not soaking them, just rinsing them. Drain well. Place them in a saute pan over med-low heat to cook off the residual water. Once the water is cooked off, increase the heat to medium and roast for 5-6 minutes. The skin will burst during this process. When the beans are aromatic and speckled with dark spots from roasting they are ready. Set them aside while you make the dashi.
MAKE THE DASHI. Combine the water and kombu in a pot over medium heat. Slowly bring it to a boil, removing the kombu just before the boiling point — when small bubbles form around the edges of the kombu it is time to remove it. When the pot comes to a boil, add the salt and the roasted soybeans. As soon as the pot returns to a boil, turn off the heat and cover the pot with a lid. Set the pot aside for 10-15 minutes to allow the flavor of the beans to infuse the liquid.
SEAR THE CABBAGE. Heat the sesame oil over medium heat and add the cabbage wedges so that they lay flat (cut side down). Cook until golden brown and crispy. Searing the cabbage on one side is enough, but searing it on both sides produces a stronger flavor. Consider what other dishes you are serving this with and decide whether a lighter or stronger soup is appropriate.
BRAISE THE CABBAGE. Add the cabbage to the dashi and bring it to a boil over high heat. As soon as it boils, reduce the heat to a gentle simmer and cook for 20-30 minutes or until the cabbage is tender. Adjust the flavor if needed with more sea salt.
SERVING THE SOUP. Place two wedges of cabbage in the center of a soup bowl and ladle the dashi and soy beans over the top. Garnish with cracked black pepper and serve hot.
SEARING THE CABBAGE. Leaving the core intact makes turning the cabbage from one side to another easier as you are searing it. After the cabbage is seared on all sides, remove it from the pan, remove the core, and cut the leaves into pieces. The core itself is also edible, but a bit tougher, so slice it thinly and add it to the soup along with the leaves.