Preheat oven to 350 degrees Fahrenheit.
Mix together the veggies, tomato paste, and miso. Spread evenly out onto a rimmed baking sheet.
Roast veggies for 40 minutes, until they are soft and beginning to get a little blackened.
Toss the roasted vegetables in with the water, shiitake mushrooms, and kombu sheet. Bring to a boil and then reduce heat to low. Simmer for 30 minutes. Strain the vegetables and mushrooms out.