Sort, rinse, and drain the dried peas.
Place kombu in bottom of 5-quart slow-cooker. Add peas and all other ingredients except for vegetable base and miso. Add water until ingredients are just covered.
With slow-cooker on high setting, begin to cook the soup mixture. Cook for 3-5 hours; cooking time will vary with different slow-cookers.
After soup has cooked for 1 hour, combine vegetable base with a small amount of soup in small cup. Add this base mixture back to soup in slow cooker. Stir thoroghly and continue to cook until ingredients are smooth and creamy.
When soup is finished cooking, turn cooker to warm setting and add miso in the same way you added the vegetable base. Stir with a wire whisk to combine, and serve.